Reference no: EM132168348

Muzi Corporation produces three products at two different plants. The cost of producing a unit at each plant is given in the following table.

Product 1

Product 2

Product 3

Plant A

R5

R6

R8

Plant B

R8

R7

R10

Each plant has the capacity to produce a total of 10 000 units. Demand for at least 6 000 units of product 1, at least 8 000 units of product 2 and at least 5 000 units of product 3 must be met. Muzi wishes to minimise costs. The decision variables are defined as follows:

Pij = the number of units of product j produced at plant i, where i = A, B and j = 1, 2, 3.

(a) Formulate the problem as a linear programming (LP) model.

(b) Solve the model using LINDO SOLVER.

Using only the initial printout of the optimal solution, answer the following questions. (This means that you may not change the relevant parameters in the model and do reruns.) Explain how you arrive at your answers.

(c) Write down the optimal solution and the associated total costs.

(d) Give the optimal solution and total costs if

(i) plant B has 9 000 units of capacity;

(ii) plant A has 12 000 units of capacity.

(e) What would the total costs be if the demand for product 2 reduces to 4 000 units?

(f) What would the cost of producing product 2 at plant A have to be for the firm to make this choice?