A coffee maker vendor has set up two coffee machines, Machine 1 and Machine 2, i

Question

A coffee maker vendor has set up two coffee machines, Machine 1 and Machine 2, inside an organization. The service cost incurred on Machine 1 and Machine 2 is $100 and $80, respectively. The production cost of coffee is $2 per mug for Machine 1 and $3 per mug for Machine 2. There is no service provided by the vendor on Sundays. The weekly production capacity is 1000 mugs for Machine 1 and 1200 mugs for Machine 2, and thereafter the machine needs to be serviced before any extra mug of coffee is to be served. Due to Christmas, the employee attendance at the organization is going to be low and only one machine has to be used to serve at least 800 mugs of coffee in that week in order to minimize the total cost.

Formulate and solve the integer programming model that could be used to determine the coffee machine which minimizes the cost (give decision variables with specific constraints, and Excel Solver solution)

Explanation / Answer

Let us assume the two decision variables are involved in this problem.

For machine 1 = x1

and machine 2 = x2

Objective is Z (minimize the cost) = 2 x1 + 3x2

subject to constraints:

1000 x1 + 1200 x2 800 (production capacity constraints)

100 x1 + 80 x2 5600 (service cost constraints)

The problem is going to be solved using solver.

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