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.

Explanation / Answer

Machine 1 has service cost $100 and Production cost is $2 per mug with capacity of 1000 mugs per week.

Therefore Total cost for machine 1 for the week is $2,100 for 1000 mugs giving $2.1 as cost per mug.

Machine 2 has service cost $80 and Production cost is $3 per mug with capacity of 1200 mugs per week.

Therefore Total cost for machine 2 for the week is $3,680 for 1200 mugs giving $3.07 as cost per mug.

At the minimum level of 800 mugs, the total cost in case of Machine 1 is $1,700 and in case of Machine 2 is $2,480.

Based on the above analysis Machine 1 is preferred.

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