1. Applied Statistical and Optimization Models
Topic 03: Reading Excel Solver Output

2. Objectives
Become more confident in entering linear programming problems into Excel.
Understand the
Answer
Sensitivity and
Limit output options

3. Reading Excel Solver Output
This was the Falcons Toys Inc.
Optimum

4. Reading Excel Solver Output
And these are the options you can choose from when using Excel solver

5. Reading Excel Solver Output
The Answer Output is Relatively Straightforward
Optimum profit of 100
Optimum output
Information on whether the constraints are met or whether there is slack

6. Reading Excel Solver Output
The Sensitivity Output is Slightly More Complex
Reduced cost tells you: The reduced cost tells how much the objective coefficient needs to change in order for a decision variable to become positive in an optimal solution.
Shadow price tells you: How much can the optimal solution be increased or decreased if we change the right hand side values (resources available) by one unit.
Allowable Increase/Decrease: Allowable amount of parameter change (price or constraint) before the shadow price changes.

7. Reading Excel Solver Output
Illustrating the Meaning of Sensitivity Analysis – What happened if the price for a Freeman Increased by 10 from PF=10 to PF=20?
The isoprofit line would have now a slope of negative 2 instead of negative 1.
At a slope of close to negative 2, the isoprofit line has almost the same slope as the cloth constraint (red) and F=8 and R=2 is still optimum.
At an (absolute) slope of greater than 2, it would make more sense to produce only Freemans (F=9) and no Ryans.

8. Reading Excel Solver Output
Illustrating the Meaning of Sensitivity Analysis – What happened if the cloth constraint was relaxed from Cmax=18 to Cmax=24?
The cloth constraint (red) would now shift parallel to the right by three units.
The optimum solution would then be to produce F=12 and R=0 with a total profit of P=120 (check with solver).
The shadow price is then 3.33 per unit of extra unit of cloth.
At more than six extra units of cloth, the shadow price would fall to zero.

9. Reading Excel Solver Output
The Limits Output
Simply tells you the optimum quantities solution for the decision variables and corresponding optimum objective function value.
It also tells you how the objective function value would change if you changed one decision variable to its upper and lower limit, holding constant the optimum value of the other decision variables.
The limits report can be thought of as a special kind of “sensitivity analysis” using limits rather than marginal changes.

10. What you Should Have Learned
Advance your linear programming skills in Excel
Run Excel solver with even more confidence
Interpret answer output, sensitivity analysis, and limits report.