Question

Question 1

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

Plant A Plant B	Product 1	Product 2	Product 3
	R5	R6	R8
	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. (2 x 2 = 4 marks)

(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?

(g) What would the new optimal solution and total costs be if

(i) The new cost of producing a unit of product 3 at plant A is R8, 50?

(ii) A new production process is introduced at plant B which reduces the cost of production of all products by R1 per unit?

(h) The workers at plant B have just completed a course on product 1 and the production manager suggests that 1 000 units of product 1 be produced at plant B. How will this affect the total cost?

Answer 1

ANSWER ;

(a) LPP solution-

Objective Function - Min Cost = R5*PA1 + R6*PA2 + R8*PA3 + R8*PB1 +R7*PB2 + R10*PB3

subject to R5+R6+R8 =10,000;

R8+R7+R10 = 10,000;

R5 + R8 >= 6000;

R6 + R7 >= 8000;

R8 + R10 >= 5000;

and Pij >=0 and Integer

(b) to solve using Solver lets take the value as R5=5; R6=6; R7=7, R8=8, R10=10;

initial solution lets take all Pij = 0; as shown below -

now setting constraints in the solver -

(c) Optimal solution is PA1 = 7000; PA2 = 0; PA3 = 3000; PB1 = 0, PB2 = 8000, PB3 = 2000;

and total cost is 135,000

(d) - (i) Plant B has 9000 units capacity ;

PA1 = 6000; PA2 = 4000; PA3 = 0; PB1 = 0, PB2 = 4000, PB3 = 5000;

and total cost is 132,000

(ii) Plant A has 12000 capacity

PA1 = 6000; PA2 = 1000; PA3 = 5000; PB1 = 0, PB2 = 7000, PB3 = 0;

and total cost is 125,000

(e) total cost = 100,000

(f) cost of producing Product 2 at Plant A is 0;

(g) (i)

Total Cost = 95,000

(h) will affect by 8000