Pedro’s Italian Food Company Pedro’s Italian Food Company offers monthly service plans, providing prepared meals that are delivered to the customers’ homes and that need only to be heated in a micro-wave or conventional oven. The target market for these meal plans includes double income families with no children and retired couples in the upper income brackets.

Pedro’s Italian Food offers three monthly plans: Standard Cuisine, Premier Cuisine and Haute Cuisine. The Standard Cuisine plan provides frozen meals that are delivered once each month, and generates a profit of €125 for each plan sold. Premier Cuisine plan provides vacuum meals that are delivered twice each month; this plan generates a profit of €140 for each monthly plan sold. The Haute Cuisine plan provides freshly prepared meals delivered on a daily basis and generates a profit of €130 for each monthly plan sold. Pedro’s Italian Food’s reputation provides the company with a market that will purchase all the meals that can be prepared.

All meals go through food preparation, cooking and finishing steps in the company’s kitchens.

After these steps, the Standard Cuisine and Premier Cuisine meals are flash frozen. The time requirements per monthly meal plan and hours available per month are presented below.

Standard cuisine products require 2 hours of preparation, 2 hours of cooking, 2 hours of finishing and 1 hour freezing. Premier consumes 2 hours of preparation, 2 hours of cooking, 3 hours preparation and 1 hour freezing. Haute Cuisine needs 1 hour preparation, 3 hours cooking, 5 hours of finishing and no freezing. Total hours available for preparation, cooking, finishing and freezing are 80, 130, 180 and 60 respectively.

For planning purposes, Pedro’s Italian Food uses linear programming to determine the most profitable number of Standard Cuisine, Premier Cuisine and Haute Cuisine monthly meal plans to produce.
Required:
1. Using the notations S = Standard Cuisine, P = Premier Cuisine and H = Haute Cuisine, state the objective function and the constraints that Pedro’s Italian Food should use to maximise profits generated by the monthly meal plans.
2. We expect certain elements of the decision problem to change in the future.

a. How would the optimal mix change if the price for Haute Cuisine were to be raised by €50 per plan sold? How would the value of the objective function be affected by the same change?

b. How would the optimal mix change if the constraint for preparation were to be eliminated?

c. How would the optimal mix change if the hours available for cooking were to be reduced by 30? How would this same change affect the objective function value?

d. What would happen with the optimal mix if the profit of Standard Cuisine were increased by €10?
3. Pedro’s Italian Food Company does not want to produce partial meals. Recalculate the optimal solution allowing for complete units only. What is the optimal product mix? What happened to the total profits? Why?

Transcribed Image Text:

Hours required Standard Cuisine Premier Cuisine Haute Cuisine Total hours available Preparation Cooking Finishing Freezing 1 1 0 180 60 235 2238 130 2278 80