Excel
| A | B | C | D | E | F | G | H |
---|-----------------|----------|--------|--------|-----------|-------------|---------|----------|---
1 | Loan | 50.000 | Year | Start | Interests | Repayment | Annuity | End |
2 | Interests p.a. | 2% | 1 | 50.000 | -1.250 | -1.750 | -3.000 | 48.250 |
3 | Annuity p.a. | 3.000 | 2 | 48.250 | -1.206 | -1.794 | -3.000 | 46.456 |
4 | Maturity | ?? | 3 | 46.456 | -1.161 | -1.839 | -3.000 | 44.618 |
5 | | | 4 | 44.618 | -1.115 | -1.885 | -3.000 | 42.733 |
| | | | | | | | |
| | | | | | | | |
21 | | | 20 | 8.094 | -202 | -2.798 | -3.000 | 5.297 |
22 | | | 21 | 5.297 | -132 | -2.868 | -3.000 | 2.429 |
23 | | | 22 | 2.429 | -61 | -2.939 | -3.000 | 0 |
The above loan of 50.000 has an interest rate of 2% and an annuity of 3.000.
In the table from C1:H23 the annual development of the remaining loan is displayed.
Based on this helper table I know that the maturity of the loan is 22 years by using the following formula in Cell B4:
B4 = COUNTA(C1:C22)
However, my question is if there is an Excel-Formula that can calculate the maturity in one cell so I do not need the helper table in C1:H23?
I'm recreating a tool I made in Excel as it's getting bigger and performance is getting out of hand.
The issue is that I only have MS Access 2013 on my work laptop and I'm fairly new to the Expression Builder in Access 2013, which has a very limited function base to be honest.
My data has duplicates on the [Location] column, meaning that, I have multiple SKUs on that warehouse location. However, some of my calculations need to be done only once per [Location]. My solution to that, in Excel, was to make a formula (see below) putting 1 only on the first appearance of that location, putting 0 on next appearances. Doing that works like a charm because summing over that [Duplicate] column while imposing multiple criteria returns the number of occurrences of the multiple criteria counting locations only once.
Now, MS Access 2013 Expression Builder has no SUM nor COUNT functions to create a calculated column emulating my [Duplicate] column from Excel. Preferably, I would just input the raw data and let Access populate the calculated fields vs also inputting the calculated fields as well, since that would defeat my original purpose of reducing the computational cost of creating my dashboard.
The question is, how would you create a calculated column, in MS Access 2013 Expression Builder to recreate the below Excel function:
= IF($D$2:$D3=$D4,0,1)
In the sake of reducing the file size (over 100K rows) I even replace the 0 by a blank character "".
Thanks in advance for your help
Y
First and foremost, understand MS Access' Expression Builder is a convenience tool to build an SQL expression. Everything in Query Design ultimately is to build an SQL query. For this reason, you have to use a set-based mentality to see data in whole sets of related tables and not cell-by-cell mindset.
Specifically, to achieve:
putting 1 only on the first appearance of that location, putting 0 on next appearances
Consider a whole set-based approach by joining on a separate, aggregate query to identify the first value of your needed grouping, then calculate needed IIF expression. Below assumes you have an autonumber or primary key field in table (a standard in relational databases):
Aggregate Query (save as a separate query, adjust columns as needed)
SELECT ColumnD, MIN(AutoNumberID) As MinID
FROM myTable
GROUP BY ColumnD
Final Query (join to original table and build final IIF expression)
SELECT m.*, IIF(agg.MinID = AutoNumberID, 1, 0) As Dup_Indicator
FROM myTable m
INNER JOIN myAggregateQuery agg
ON m.[ColumnD] = agg.ColumnD
To demonstrate with random data:
Original
| ID | GROUP | INT | NUM | CHAR | BOOL | DATE |
|----|--------|-----|--------------|------|-------|------------|
| 1 | r | 9 | 1.424490258 | B6z | TRUE | 7/4/1994 |
| 2 | stata | 10 | 2.591235683 | h7J | FALSE | 10/5/1971 |
| 3 | spss | 6 | 0.560461966 | Hrn | TRUE | 11/27/1990 |
| 4 | stata | 10 | -1.499272175 | eXL | FALSE | 4/17/2010 |
| 5 | stata | 15 | 1.470269177 | Vas | TRUE | 6/13/2010 |
| 6 | r | 14 | -0.072238898 | puP | TRUE | 4/1/1994 |
| 7 | julia | 2 | -1.370405263 | S2l | FALSE | 12/11/1999 |
| 8 | spss | 6 | -0.153684675 | mAw | FALSE | 7/28/1977 |
| 9 | spss | 10 | -0.861482674 | cxC | FALSE | 7/17/1994 |
| 10 | spss | 2 | -0.817222582 | GRn | FALSE | 10/19/2012 |
| 11 | stata | 2 | 0.949287754 | xgc | TRUE | 1/18/2003 |
| 12 | stata | 5 | -1.580841322 | Y1D | TRUE | 6/3/2011 |
| 13 | r | 14 | -1.671303816 | JCP | FALSE | 5/15/1981 |
| 14 | r | 7 | 0.904181025 | Rct | TRUE | 7/24/1977 |
| 15 | stata | 10 | -1.198211174 | qJY | FALSE | 5/6/1982 |
| 16 | julia | 10 | -0.265808162 | 10s | FALSE | 3/18/1975 |
| 17 | r | 13 | -0.264955027 | 8Md | TRUE | 6/11/1974 |
| 18 | r | 4 | 0.518302149 | 4KW | FALSE | 9/12/1980 |
| 19 | r | 5 | -0.053620183 | 8An | FALSE | 4/17/2004 |
| 20 | r | 14 | -0.359197116 | F8Q | TRUE | 6/14/2005 |
| 21 | spss | 11 | -2.211875193 | AgS | TRUE | 4/11/1973 |
| 22 | stata | 4 | -1.718749471 | Zqr | FALSE | 2/20/1999 |
| 23 | python | 10 | 1.207878576 | tcC | FALSE | 4/18/2008 |
| 24 | stata | 11 | 0.548902226 | PFJ | TRUE | 9/20/1994 |
| 25 | stata | 6 | 1.479125922 | 7a7 | FALSE | 3/2/1989 |
| 26 | python | 10 | -0.437245299 | r32 | TRUE | 6/7/1997 |
| 27 | sas | 14 | 0.404746106 | 6NJ | TRUE | 9/23/2013 |
| 28 | stata | 8 | 2.206741458 | Ive | TRUE | 5/26/2008 |
| 29 | spss | 12 | -0.470694096 | dPS | TRUE | 5/4/1983 |
| 30 | sas | 15 | -0.57169507 | yle | TRUE | 6/20/1979 |
SQL (uses aggregate in subquery but can be a stored query)
SELECT r.*, IIF(sub.MinID = r.ID,1, 0) AS Dup
FROM Random_Data r
LEFT JOIN
(
SELECT r.GROUP, MIN(r.ID) As MinID
FROM Random_Data r
GROUP BY r.Group
) sub
ON r.[Group] = sub.[GROUP]
Output (notice the first GROUP value is tagged 1, all else 0)
| ID | GROUP | INT | NUM | CHAR | BOOL | DATE | Dup |
|----|--------|-----|--------------|------|-------|------------|-----|
| 1 | r | 9 | 1.424490258 | B6z | TRUE | 7/4/1994 | 1 |
| 2 | stata | 10 | 2.591235683 | h7J | FALSE | 10/5/1971 | 1 |
| 3 | spss | 6 | 0.560461966 | Hrn | TRUE | 11/27/1990 | 1 |
| 4 | stata | 10 | -1.499272175 | eXL | FALSE | 4/17/2010 | 0 |
| 5 | stata | 15 | 1.470269177 | Vas | TRUE | 6/13/2010 | 0 |
| 6 | r | 14 | -0.072238898 | puP | TRUE | 4/1/1994 | 0 |
| 7 | julia | 2 | -1.370405263 | S2l | FALSE | 12/11/1999 | 1 |
| 8 | spss | 6 | -0.153684675 | mAw | FALSE | 7/28/1977 | 0 |
| 9 | spss | 10 | -0.861482674 | cxC | FALSE | 7/17/1994 | 0 |
| 10 | spss | 2 | -0.817222582 | GRn | FALSE | 10/19/2012 | 0 |
| 11 | stata | 2 | 0.949287754 | xgc | TRUE | 1/18/2003 | 0 |
| 12 | stata | 5 | -1.580841322 | Y1D | TRUE | 6/3/2011 | 0 |
| 13 | r | 14 | -1.671303816 | JCP | FALSE | 5/15/1981 | 0 |
| 14 | r | 7 | 0.904181025 | Rct | TRUE | 7/24/1977 | 0 |
| 15 | stata | 10 | -1.198211174 | qJY | FALSE | 5/6/1982 | 0 |
| 16 | julia | 10 | -0.265808162 | 10s | FALSE | 3/18/1975 | 0 |
| 17 | r | 13 | -0.264955027 | 8Md | TRUE | 6/11/1974 | 0 |
| 18 | r | 4 | 0.518302149 | 4KW | FALSE | 9/12/1980 | 0 |
| 19 | r | 5 | -0.053620183 | 8An | FALSE | 4/17/2004 | 0 |
| 20 | r | 14 | -0.359197116 | F8Q | TRUE | 6/14/2005 | 0 |
| 21 | spss | 11 | -2.211875193 | AgS | TRUE | 4/11/1973 | 0 |
| 22 | stata | 4 | -1.718749471 | Zqr | FALSE | 2/20/1999 | 0 |
| 23 | python | 10 | 1.207878576 | tcC | FALSE | 4/18/2008 | 1 |
| 24 | stata | 11 | 0.548902226 | PFJ | TRUE | 9/20/1994 | 0 |
| 25 | stata | 6 | 1.479125922 | 7a7 | FALSE | 3/2/1989 | 0 |
| 26 | python | 10 | -0.437245299 | r32 | TRUE | 6/7/1997 | 0 |
| 27 | sas | 14 | 0.404746106 | 6NJ | TRUE | 9/23/2013 | 1 |
| 28 | stata | 8 | 2.206741458 | Ive | TRUE | 5/26/2008 | 0 |
| 29 | spss | 12 | -0.470694096 | dPS | TRUE | 5/4/1983 | 0 |
| 30 | sas | 15 | -0.57169507 | yle | TRUE | 6/20/1979 | 0 |
I am new to this site and haven't done much in Excel of decades (yes, decades), so I forgotten more than I know now.
Background: I am working on a simple pay sheet checking spreadsheet. One Worksheet is input timesheet for data entry, the complex one does all the calculations (Hourly rate; shift loading; tax formula, etc.) and the final worksheet presents the results in the same format as pay slip. Having finished the complex formulas in the calculation sheet, I am now stuck on condensing the results for the final results on the last sheet. I have try numerous functions including: vlookup, index, match, rank.eq, small and others, as per examples of other question on this site. Sample data is:
+----+-----------------------------------------------------+----------------+------------+--------------+--------+--------+-----+--------+
| | A | B | C | D | E | F | G | H |
+----+-----------------------------------------------------+----------------+------------+--------------+--------+--------+-----+--------+
| 1 | Sample data: | | | | | | | |
| 2 | Monday | Ordinary Hours | 30/04/2018 | Day Shift | 10.85 | 21.85 | 1 | 237.07 |
| 3 | Tuesday | Ordinary Hours | 1/05/2018 | | | 21.85 | 1 | |
| 4 | Wednesday | Ordinary Hours | 2/05/2018 | | | 21.85 | 1 | |
| 5 | Thursday | Ordinary Hours | 3/05/2018 | | | 21.85 | 1 | |
| 6 | Friday | Ordinary Hours | 4/05/2018 | | | 21.85 | 1 | |
| 7 | | | | | | | | |
| 8 | | | | | | | | |
| 9 | Monday | Ordinary Hours | 7/05/2018 | | | 21.85 | 1 | |
| 10 | Tuesday | Ordinary Hours | 8/05/2018 | | | 21.85 | 1 | |
| 11 | Wednesday | Ordinary Hours | 9/05/2018 | Day Shift | 10.85 | 21.85 | 1 | 237.07 |
| 12 | Thursday | Ordinary Hours | 10/05/2018 | Day Shift | 10.85 | 21.85 | 1 | 237.07 |
| 13 | Friday | Ordinary Hours | 11/05/2018 | | | 21.85 | 1 | |
| 14 | | | | | | | | |
| 15 | Monday | Overtime 1.5 | 30/04/2018 | | | 21.85 | 1.5 | |
| 16 | Tuesday | Overtime 1.5 | 1/05/2018 | Overtime 1.5 | 2 | 21.85 | 1.5 | 65.55 |
| 17 | Wednesday | Overtime 1.5 | 2/05/2018 | | | 21.85 | 1.5 | |
| 18 | Thursday | Overtime 1.5 | 3/05/2018 | | | 21.85 | 1.5 | |
| 19 | Friday | Overtime 1.5 | 4/05/2018 | | | 21.85 | 1.5 | |
| 20 | Saturday | Overtime 1.5 | 5/05/2018 | | | 21.85 | 1.5 | |
| 21 | | | | | | | | |
| 22 | Monday | Overtime 1.5 | 7/05/2018 | | | 21.85 | 1.5 | |
| 23 | Tuesday | Overtime 1.5 | 8/05/2018 | | | 21.85 | 1.5 | |
| 24 | Wednesday | Overtime 1.5 | 9/05/2018 | | | 21.85 | 1.5 | |
| 25 | Thursday | Overtime 1.5 | 10/05/2018 | | | 21.85 | 1.5 | |
| 26 | Friday | Overtime 1.5 | 11/05/2018 | | | 21.85 | 1.5 | |
| 27 | Saturday | Overtime 1.5 | 12/05/2018 | | | 21.85 | 1.5 | |
| 28 | | | | | | | | |
| 29 | | | | | | | | |
| 30 | Required result on separate sheet in same workbook: | | | | | | | |
| 31 | Taxable Allowances | Comments | Qty | Rate | Factor | Amount | | |
| 32 | Ordinary Hours | 30/04/2018 | 10.85 | 21.85 | 1 | 237.07 | | |
| 33 | Ordinary Hours | 9/05/2018 | 10.85 | 21.85 | 1 | 237.07 | | |
| 34 | Ordinary Hours | 10/05/2018 | 10.85 | 21.85 | 1 | 237.07 | | |
| 35 | Overtime 1.5 | 1/05/2018 | 2 | 21.85 | 1.5 | 65.55 | | |
| 36 | | | | | | | | |
| 37 | | | | | | | | |
| 38 | | | | | | | | |
| 39 | | | | | | | | |
| 40 | | | | | | | | |
+----+-----------------------------------------------------+----------------+------------+--------------+--------+--------+-----+--------+
I am working in Excel 2016. I am trying to figure out how many projects I have that have not had any part of it started. For instance if my project id is 203784 and it has 3 parts to it where 2 are Complete and 1 was Not Started. I would not want to count that. If the project had 3 parts and 2 were Not Started 1 was assigned. I would want to count that as 1. Thank you in advance you your assistance.
+----+------------+------------------+-------------+
| | A | B | C |
+----+------------+------------------+-------------+
| 1 | Project ID | Position | Status |
| 2 | 203784 | Staff | Complete |
| 3 | 203784 | Staff | Complete |
| 4 | 203784 | Staff | Not Started |
| 5 | 203785 | Maintenance | Complete |
| 6 | 203785 | Maintenance | In Progress |
| 7 | 203786 | Grounds | Complete |
| 8 | 203787 | Nurse | Complete |
| 9 | 203788 | Teacher | Complete |
| 10 | 203788 | Teacher | Complete |
| 11 | 203788 | Teacher | Complete |
| 12 | 203789 | Transportation | Complete |
| 13 | 203789 | Transportation | Complete |
| 14 | 203789 | Transportation | Complete |
| 15 | 203790 | Evacuation | Complete |
| 16 | 203790 | Evacuation | Complete |
| 17 | 203791 | Implementation | Complete |
| 18 | 203792 | Knowledge Base | Not Started |
| 19 | 203792 | Knowledge Base | Not Started |
| 20 | 203793 | Janitor | Not Started |
| 21 | 203794 | Public Relations | In Progress |
| 22 | 203795 | HR | Complete |
| 23 | 203796 | Admin | Complete |
+----+------------+------------------+-------------+
In this example. I would only want the count to show a total of 2. For project numbers 203792 and 203793.
One way would be to add a column (say Count) populated as:
=COUNTIFS(A:A,A2,C:C,"Complete")+COUNTIFS(A:A,A2,C:C,"In Progress")
and then create a PivotTable with Count as Filters and Project ID for Rows. Select 0 for the filter.
Oil Blending
An oil company produces three brands of oil: Regular, Multigrade, and
Supreme. Each brand of oil is composed of one or more of four crude stocks, each having a different lubrication index. The relevant data concerning the crude stocks are as follows.
+-------------+-------------------+------------------+--------------------------+
| Crude Stock | Lubrication Index | Cost (€/barrell) | Supply per day (barrels) |
+-------------+-------------------+------------------+--------------------------+
| 1 | 20 | 7,10 | 1000 |
+-------------+-------------------+------------------+--------------------------+
| 2 | 40 | 8,50 | 1100 |
+-------------+-------------------+------------------+--------------------------+
| 3 | 30 | 7,70 | 1200 |
+-------------+-------------------+------------------+--------------------------+
| 4 | 55 | 9,00 | 1100 |
+-------------+-------------------+------------------+--------------------------+
Each brand of oil must meet a minimum standard for a lubrication index, and each brand
thus sells at a different price. The relevant data concerning the three brands of oil are as
follows.
+------------+---------------------------+---------------+--------------+
| Brand | Minimum Lubrication index | Selling price | Daily demand |
+------------+---------------------------+---------------+--------------+
| Regular | 25 | 8,50 | 2000 |
+------------+---------------------------+---------------+--------------+
| Multigrade | 35 | 9,00 | 1500 |
+------------+---------------------------+---------------+--------------+
| Supreme | 50 | 10,00 | 750 |
+------------+---------------------------+---------------+--------------+
Determine an optimal output plan for a single day, assuming that production can be either
sold or else stored at negligible cost.
The daily demand figures are subject to alternative interpretations. Investigate the
following:
(a) The daily demands represent potential sales. In other words, the model should contain demand ceilings (upper limits). What is the optimal profit?
(b) The daily demands are strict obligations. In other words, the model should contain demand constraints that are met precisely. What is the optimal profit?
(c) The daily demands represent minimum sales commitments, but all output can be sold. In other words, the model should permit production to exceed the daily commitments. What is the optimal profit?
QUESTION
I've been able to construct the following model in Excel and solve it via OpenSolver, but I'm only able to integrate the mix for the Regular Oil.
I'm trying to work my way through the book Optimization Modeling with Spreadsheets by Kenneth R. Baker but I'm stuck with this exercise. While I could transfer the logic from another blending problem I'm not sure how to construct the model for multiple blendings at once.
I modeled the problem as a minimization problem on the cost of the different crude stocks. Using the Lubrication Index data I built the constraint for the R-Lub Index as a linear constraint. So far the answer seems to be right for the Regular Oil. However using this approach I've no idea how to include even the second Multigrade Oil.
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Decision Variables | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | C1 | C2 | C3 | C4 | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Inputs | 1000 | 0 | 1000 | 0 | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Objective Function | | | | | | Total | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Cost | 7,10 € | 8,50 € | 7,70 € | 9,00 € | | 14.800,00 € | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Constraints | | | | | | LHS | | RHS |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C1 supply | 1 | | | | | 1000 | <= | 1000 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C2 supply | | 1 | | | | 0 | <= | 1100 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C3 supply | | | 1 | | | 1000 | <= | 1200 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C4 supply | | | | 1 | | 0 | <= | 1100 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Lub Index | -5 | 15 | 5 | 30 | | 0 | >= | 0 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Output | 1 | 1 | 1 | 1 | | 2000 | = | 2000 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Blending Data | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Lub | 20 | 40 | 30 | 55 | | 25 | >= | 25 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
Here is the model with Excel formulars:
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Decision Variables | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | C1 | C2 | C3 | C4 | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Inputs | 1000 | 0 | 1000 | 0 | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Objective Function | | | | | | Total | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Cost | 7,1 | 8,5 | 7,7 | 9 | | =SUMMENPRODUKT(B5:E5;B8:E8) | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Constraints | | | | | | LHS | | RHS |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C1 supply | 1 | | | | | =SUMMENPRODUKT($B$5:$E$5;B11:E11) | <= | 1000 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C2 supply | | 1 | | | | =SUMMENPRODUKT($B$5:$E$5;B12:E12) | <= | 1100 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C3 supply | | | 1 | | | =SUMMENPRODUKT($B$5:$E$5;B13:E13) | <= | 1200 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C4 supply | | | | 1 | | =SUMMENPRODUKT($B$5:$E$5;B14:E14) | <= | 1100 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Lub Index | -5 | 15 | 5 | 30 | | =SUMMENPRODUKT($B$5:$E$5;B15:E15) | >= | 0 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Output | 1 | 1 | 1 | 1 | | =SUMMENPRODUKT($B$5:$E$5;B16:E16) | = | 2000 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Blending Data | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Lub | 20 | 40 | 30 | 55 | | =SUMMENPRODUKT($B$5:$E$5;B19:E19)/SUMME($B$5:$E$5) | >= | 25 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
A nudge in the right direction would be a tremendous help.
I think you want your objective to be Profit, which I would define as the sum of sales value - sum of cost.
To include all blends, develop calculations for Volume produced, Lube Index, Cost, and Value for each blend. Apply constraints for volume of stock used, volume produced, and lube index, and optimize for Profit.
I put together the model as follows ...
Columns A through D is the information you provided.
The 10's in G2:J5 are seed values for the stock volumes used in each blend. Solver will manipulate these.
Column K contains the total product volume produced. These will be constrained in different ways, as per your investigation (a), (b), and (c). It is =SUM(G3:J3) filled down.
Column L is the Lube Index for the product. As you noted, it is a linear blend - this is typically not true for blending problems. These values will be constrained in Solver. It is {=SUMPRODUCT(G3:J3,TRANSPOSE($B$2:$B$5))/$K3} filled down. Note that it is a Control-Shift-Enter (CSE) formula, required because of the TRANSPOSE.
Column M is the cost of the stock used to create the product. This is used in the Profit calculation. It is {=SUMPRODUCT(G3:J3,TRANSPOSE($C$2:$C$5))}, filled down. This is also a CSE formula.
Column N is the value of the product produced. This is used in the Profit calculation. It is =K3*C8 filled down.
Row 7 is the total stock volume used to generate all blends. These values will be constrained in Solver. It is =SUM(G3:G5), filled to the right.
The profit calculation is =SUM(N3:N5)-SUM(M3:M5).
Below is a snap of the Solver dialog box ...
It does the following ...
The objective is to maximize profit.
It will do this by manipulating the amount of stock that goes into each blend.
The first four constraints ($G$7 through $J$7) ensure the amount of stock available is not violated.
The next three constraints ($K$3 through $K$5) are for case (a) - make no more than product than there is demand.
The last three constraints ($L$3 through $L$5) make sure the lube index meets the minimum specification.
Not shown - I selected options for GRG Nonlinear and selected "Use Multistart" and deselected "Require Bounds on Variables".
Below is the result for case (a) ...
For case (b), change the constraints on Column K to be "=" instead of "<=". Below is the result ...
For case (c), change the constraints on Column K to be ">=". Below is the result ...
I think I came up with a solution, but I'm unsure if this is correct.
| Decision Variables | | | | | | | | | | | | | | | | |
|--------------------|---------|--------|--------|--------|-------------|--------|--------|--------|--------|--------|--------|--------|---|--------------------------------|----|------|
| | C1R | C1M | C1S | C2R | C2M | C2S | C3R | C3M | C3S | C4R | C4M | C4S | | | | |
| Inputs | 1000 | 0 | 0 | 800 | 0 | 300 | 0 | 1200 | 0 | 200 | 300 | 600 | | | | |
| | | | | | | | | | | | | | | | | |
| Objective Function | | | | | | | | | | | | | | Total Profit (Selling - Cost) | | |
| Cost | 7,10 € | 7,10 € | 7,10 € | 8,50 € | 8,50 € | 8,50 € | 7,70 € | 7,70 € | 7,70 € | 9,00 € | 9,00 € | 9,00 € | | 3.910,00 € | | |
| | | | | | | | | | | | | | | | | |
| Constraints | | | | | | | | | | | | | | LHS | | RHS |
| Regular | -5 | | | 15 | | | 5 | | | 30 | | | | 13000 | >= | 0 |
| Multi | | -15 | | | 5 | | | -5 | | | 20 | | | 0 | >= | 0 |
| Supreme | | | -30 | | | -10 | | | -20 | | | 5 | | 0 | >= | 0 |
| C1 Supply | 1 | 1 | 1 | | | | | | | | | | | 1000 | <= | 1000 |
| C2 Supply | | | | 1 | 1 | 1 | | | | | | | | 1100 | <= | 1100 |
| C3 Supply | | | | | | | 1 | 1 | 1 | | | | | 1200 | <= | 1200 |
| C4 Supply | | | | | | | | | | 1 | 1 | 1 | | 1100 | <= | 1100 |
| Regular Demand | 1 | | | 1 | | | 1 | | | 1 | | | | 2000 | >= | 2000 |
| Multi Demand | | 1 | | | 1 | | | 1 | | | 1 | | | 1500 | >= | 1500 |
| Supreme Demand | | | 1 | | | 1 | | | 1 | | | 1 | | 900 | >= | 750 |
| | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | |
| Selling | | | | | | | | | | | | | | | | |
| Regular | 8,50 € | x | 2000 | = | 17.000,00 € | | | | | | | | | | | |
| Multi | 9,00 € | x | 1500 | = | 13.500,00 € | | | | | | | | | | | |
| Supreme | 10,00 € | x | 900 | = | 9.000,00 € | | | | | | | | | | | |
| | | | | | 39.500,00 € | | | | | | | | | | | |