Question

A chocolate making company largely produces one particular type of crunchy chocolate bar. Only one of two machines, Machine-1 or Machine-2, can be used to produce this chocolate bar on any given day. The maintenance costs incurred on these two machines per day are $100 and $120, respectively. The manufacturing cost per chocolate bar is $2.5 for Machine-1 and $2 for Machine-2. The maximum daily production capacities for Machine-1 and Machine-2 are 1100 and 1250, respectively. Demand requires that at least 1000 chocolate bars be produced per day. Develop and solve a binary integer programming model for minimizing the total cost. Write all the constraints and objective function. Solve using Solver and write the answer for how many chocolate bars to be produced by each machine and if machine 1 or 2 will be used for the minimum cost

Answer 1

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Answer

Integer programming formulation

Solution

I have used excel solver to solve the problem. I have attached screenshots of Input data, formulas and constraints used along with the optimal solution.

Here, Machine 2 will be selected to produce 1000 units to minimize the cost. Cost = $ 2120

1. Snapshot of Input Data

2. Snapshot of formulas used

3. Snapshot of Constraints used

4. Snapshot of Optimal Solution