8. (15 points) A coffee maker vendor has set up two coffee machines, Machine 1 a

Question

8. (15 points) 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 an integer programming model, and solve it using EXCEL.

Explanation / Answer

x1 = Number of cups produced by Machine 1

x2 = Number of cups produced by Machine 2

Since the objective is to minimize the total cost

Z = 2x1 + 3x2

x1<= 1000

x2<=1200

x1>=800

x1>=0, x2>=0

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