You started a new company for catering high-quality/high-demand meal types A, B

Question

You started a new company for catering high-quality/high-demand meal types A, B and C directly to the customers. Before giving the company a start, you estimated your production capabilities to create a feasible daily production plan that would yield a maximum profit. Each type of meal will be cooked, packed and then delivered by your company. The meals are to be cooked and delivered on the same day. The total number of hours available for cooking is estimated to be 4, for packaging is 2, and for delivery is 2. 10 portions of meal A require one hour to be cooked. The packing and delivering rates for meal A are respectively 20 and 30 portions per hour. Ingredients required for 1 portion of meal A cost $1, and each packaged portion will sell at $7. Meal B takes a bit more time to get prepared. It requires 1 hour for the cooking team to prepare 5 portions of it. Its packing and delivery rates are both 15 portions per hour. This meal will sell at $12 per portion and the cost of its ingredients is $2 per portion. Finally, 15 portions of meal C can be cooked per hour, 25 portions can be packed per hour and 30 portions can be delivered in one hour. The selling price of meal C will be $5 per portion whereas the ingredients will cost $0.5 per portion. The demand for each meal type is at most 20, 10, and 30, respectively for meal types A, B and C. Formulate a linear programming problem to determine the best combination of meals to gain a maximum profit. Clearly define your decision variables, objective and constraints.

Explanation / Answer

Total number of meals produced;be

A B and C;

maximuze profit = 7A+12B+5C-1A-2B-0.5C=6A+10B+4.5C;

A<= 20; B<=10; C<=30;

A/10+B/5+C/15 <=4; Cooking time;

A/20+B/15+C/25<=2; Packing time;

A/30+B/15+C/30<=2; Dilevery time;

Maximum profit will be when A= 8; B = ; C = 30 ;

and maximum profit is 243

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