1. Linear Programming
Excel Solver

2. The Linear Programming Model
MAX 8X1 + 5X2
s.t. 2X1 + 1X2 ≤ (Plastic)
3X1 + 4X2 ≤ (Prod. Time)
X X2 ≤ (Total Prod.)
X X2 ≤ (Mix)
All x’s ≥ 0

3. Setting Up the Excel Spreadsheet
Use one column for each decision variable and label each column.
Leave a blank row where the results will be calculated – row of “Changing Cells” and one more blank row below that
Label each row (changing cells, objective function and constraints) to the left with a brief description.
Leave one column in between the column for the last variable and the sign of the constraint for the total of left hand side.
Label the row as Total LHS (for left hand side)

4. Input Coefficients/ Label Rows
Changing Cells Label
Changing Cells
Where results will be given
Label for
Left Hand Side Total
Objective Function
Label
Constraint
Labels
Coefficients

5. Enter SUMPRODUCT Formula for the Total Proift
=SUMPRODUCT($C$4:$D$4,C6:D6)
is equivalent to
=$C$4*C6+$D$4*D6
Highlight cells C4 and D4 and press the F4 function key to enter $ signs
Highlight cells C6 and D6

6. Drag SUMPRODUCT Formula Down to get LHS Totals
Drag cell E6 down to
cells E7:E10 +

7. Go to Tools Select Solver
Note: If Solver is not in Tools menu, select Add-Ins from Tools menu and check Solver.
3. The Changing Cells are the cells containing the decision variables – Highlight cells C4 and D4.
$C$4:$D$4
$E$6
1. Target cell is the cell that contains object function value – Click cell E6.
2. Click Max or Min (Default is Max).
4. Click Add to add constraints.

8. Types of Constraints
There are 3 types of functional constraints that can be added:
“≤”
“=”
“≥”
There are also 2 other constraints in Solver that deal with requiring the value of a decision variable to be:
Integer
Binary

9. Adding A Functional Constraint
The general approach is:
Click on a cell reference containing a total LHS value
$E$7
Click on the cell reference containing the corresponding RHS value
$G$7
≤ = ≥
Click OK if no more constraints are to be entered
Click Add if more constraints are to be entered

10. Adding Several Constraints Simulataneously
If several consecutive constraints all have the same relation (“≤”, “=”, or “≥”) these can be entered all at once by:
Highlighting the set of total LHS values
Choosing the relationship
Highlighting the corresponding set of RHS values.
$E$7:$E$10
<=
$G$7:$G$10
This is what we enter in the example given here; then we click OK.

11. Clicking Options
We must finally say that the problem is to be solved as a linear program and that the variables are “≥ 0”. This is done in the Options dialogue box.

12. The Options Dialogue Box
Click OK
Check
Assume Linear Model
Check
Assume Non-Negative
Most of the rest of the entries deal with integer and nonlinear models.

13. Click Solve
Click
Solve

14. Solver Solution Optimal Solution Optimal Objective Function Value
Highlight
Answer
Sensitivity
Click OK

15. The Answer Report Optimal Objective Function Value Optimal Solution
Total LHS Values
Difference
Between
RHS - LHS

16. The Sensitivity Report
The amount the
corresponding
objective function
coefficient can
increase or decrease
without changing
the optimal solution
The Objective
Coefficients Input
Effect on
objective function
if X ≥ 1 is added
Optimal
Solution
The RHS
Coefficients Input
Total LHS
Value
The amount the
objective function
would change
with 1 more unit
on the RHS
The amount the
RHS value can
increase or decrease
without changing
the shadow price

17. Notes on Sensitivity Report Output
1E+30 is Excel’s way of saying “infinity”
Allowable Increases and Decreases apply to changing that one coefficient only – keeping all of the other coefficients the same.
Reduced Cost has many meanings:
How would the objective function be affected if the variable had to assume a value of at least 1
How much would the objective function coefficient have to change before it is economically beneficial for the corresponding variable to be positive.

18. Review How to set up an Excel spreadsheet to solve a linear program
Filling in the Solver dialogue box.
How to “Add Constraints”
Filling in the Options dialogue box
Reading and interpreting:
Excel Output
The Answer Report
The Sensitivity Report