Toms Inc. makes two salsa products: Western Foods salsa and Mexico City salsa. Essentially, the two products have different blends of whole tomatoes, tomato sauce, and tomato paste. A jar of Western Foods salsa uses 5 ounce of whole tomatoes, 3 ounces of tomato sauce, and 2 ounces of tomato paste. A jar of Mexico City salsa consists of 7 ounces of whole tomatoes, 1 ounce of tomato sauce, and 2 ounces of tomato paste.

For the current production period Toms Inc. can purchase up to 4480 ounces of whole tomatoes, 2080 ounces of tomato sauce, and 1600 ounces of tomato paste. Toms Inc. makes a profit of $1.00 per jar of Western Foods salsa and $1.25 per jar of Mexico City salsa. The following linear optimization model was used to determine the mix of salsa products that will maximize the total profit contribution.

Let

W be the number of jars of Western Foods Salsa

M be the number of jars of Mexico City Salsa

Maximize 1W + 1.25M

s.t.

5W + 7M 4480 (Whole tomatoes)

3W + 1M 2080 (Tomato sauce)

2W + 2M 1600 (Tomato paste)

W, M 0

The problem was solved in Excel and the sensitivity report is shown below. Answer the following questions based on the sensitivity report. (If a question cant be answered using the sensitivity report say so. You dont need to change the model and re-solve it.)

a) How many jars of Western Foods Salsa and how many Mexico City Salsa should Toms produce?

b) What is the profit of the optimal solution?

c) Which constraints are non-binding?

d) Calculate the slack variable for all the constraints.

e) Would the optimal solution change if the profit of a jar of Western Foods salsa changes to $1.2?

f) What the new total profit (objective value) would be if the profit of a jar of Western Foods salsa changes to $1.2?

g) How much less profit would Toms make if they had 100 fewer ounces of tomato sauce?

h) Would the optimal solution change if they had 100 fewer ounces of tomato sauce?

i) How would Toms profit change if they 500 more ounces of tomato sauce?

j) Report and interpret the shadow price values.

Microsoft Excel 11.0 Sensitivity Report Adjustable Cells Cell Name $C$17 Western Foods Salsa $D$17 Mexico City Salsa Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 560 0.000 1.00 0.107 0.25 240 0.000 1.25 0.25 0.15 Constraints Cell Name $K$10 Whole Tomatoes $K$11 Tomato Sauce $K$12 Tomato Paste Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 4480 0.125 4480 1120 160 1920 0.000 2080 1E+30 160 1600 0.187 1600 40 320 Microsoft Excel 11.0 Sensitivity Report Adjustable Cells Cell Name $C$17 Western Foods Salsa $D$17 Mexico City Salsa Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 560 0.000 1.00 0.107 0.25 240 0.000 1.25 0.25 0.15 Constraints Cell Name $K$10 Whole Tomatoes $K$11 Tomato Sauce $K$12 Tomato Paste Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 4480 0.125 4480 1120 160 1920 0.000 2080 1E+30 160 1600 0.187 1600 40 320