Question

Problem 3. Tom's Inc, makes two salse prelucts 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. Alar of Mexico City sale consists of 7 ounces of whole tomatoes, 1 ounce of tomato sauce, and 2 ounces of tomato paste. For the current production period Tom's Inc. can purchase up to 4480 ounces of whole tomatoes 2080 ounces of tomato sauce, and 1600 ounces of tomato paste. Tom's 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 IW + 1.25M s.. 5W + 7M s 4.480 (Whole tomatoes) 3W + IMs 2080 (Tomato sauce) 2W + 2M s 1600 (Tomato paste) W.M20 The problem was solved in Excel and the sensitivity report is shown below. Answer the following questions based on the sensitivity report. (a guestion can't be answered using the sensitivity report say so. You don't need to change the model and solve it.) Microsoft Excel 11.0 Sensitivity Report Adjustable Cells Cell Name SCS17 Western Foods Salsa SOS17 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 SKS10 Whole Tomatoes SK$11 Tomato Sauce SK$12 Tomato Paste Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 4480 0.125 4480 1120 160 19200.000 2080 1E+30 160 1600 0.187 1600 40 3 20 a) How many jars of Western Foods Salsa should Tom's produce? b) How many jars of Mexico City Salsa should Tom's produce? c) What is the profit of the optimal solution? d) Which constraints are non-binding? Would the optimal solution change if the profit of a jar of Western Foods salsa changes to $129 What the new total profit (objective value) would be if the profit of a jar of Western Foods sale changes to $1.2? w o uld be the value of 30 more ounces of tomato paste? (Refer to the definition of price). it would Tom's make if they had 100 fewer ounces of tomato h) How much less profit would Tom's make if they had 100 feu How would Tom's profit change if they 300 more ounces of tomato How would Tom's profit change if they had more ounces of whole to

Answer 1

You have asked a question with multiple sub parts, in the same post. I have addressed the first four. Please post the balance sub parts separately.

Part (a)

Final value of Western Food Salsa = 560

Part (b)

Final value of Mexico City Salsa = 240

Part (c)

Profit = 1 x 560 + 1.25 x 240 = 860

Part (d)

The first (whole tomatoes) and the third constraint (tomato sauce) are binding. These constraints have non zero shadow price and binding.