4. 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

Question

Karli Wall

Business

25 October, 18:56

4. 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

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Answers (1)

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Felipe Koch · Answer 1

An example of a linear (integer) programming problem

Explanation:

We infer the following:

Let the number of mugs produced by machine 1 be represented by X,

Since only one machine is to be used in the week of Christmas, this constraints should apply for machine-1;

Constraints

Production cost≤ $2,

Service Incurred cost≤$100,

Production capacity (excluding sunday) ≥ 800 mugs served,

Objective Function

Minimise cost: XService cost + XProduction cost

Minimise: 100x + 20x