Question

Metro Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches-- ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker .45 minutes to assemble, a bologna sandwich requires .41 minutes, and a chicken salad sandwich requires .50 minutes to make.

The company has 960 available minutes each night for sandwich assembly. Vending machine capacity is available for 2,000 sandwiches each day. The profit for a ham and cheese sandwich is $.35, the profit for a bologna sandwich is $.42, and the profit for a chicken salad sandwich is $.37. The company knows from past sales records that its customers buy as many ham and cheese sandwiches as the other two sandwiches combined, if not more so, but customers need a variety of sandwiches available, so Metro stocks at least 200 of each.

Metro management wants to know how many of each sandwich it should stock to maximize profit.

Formulate a linear programming model for this problem.

Answer 1

Let x=ham and cheese sandwich

Y=bolunga sandwich

Z=chicken salad sandwich

Objective function

Max F=0.35x+0.42y+0.37z

Constraints

0.45x+0.41y+0 50z<=960 (labour hours)

x+y+z=2000

x>=200

y>=200

z>=200

x>=y+z

x,y,z>0