Question

Case Study – 3

National Cable Factory is one of the leading manufacturer of Medium Voltage power cables (MV Cables) and Low Voltage power cables (LV Cables) in Oman. The market demand survey conducted by the company found that the minimum demand per week for MV cables is 30 and the minimum demand for LV cables is only 10. MV cables requires five production hours and five skilled labour hours to produce one unit whereas LV cables require three production hours and six skilled labour hours to produce one unit. The total production hours and skilled labour hours available per week are 180 and 240 respectively. Material constraint indicates the limitations of only 100 units for the requirement of two units of material per unit of MV Cables and LV Cables each. LV cables generates a contribution of RO 350 per unit and MV cable contributes RO 200 per unit.

The company wishes to adopt Linear Programming Model to determine the optimum production mix of MV Cables and LV Cables. As a Production Manager, advise National Cable Factory how many units of Medium Voltage power cables (MV Cables) and Low Voltage power cables (LV Cables) need to be manufactured in a week. Also, calculate the maximum profit earned by National Cable Factory per week.

(3+5+2 = 10 Marks)

Answer 1

Let the number of units of MV cable to be manufactured be X and of LV Cables be Y.

Now, we need to maximize the profit.

The Objective function will be

Maximize Z = 200X + 350Y

Since, the number of cables maufactured cannot be negative, we will also have non-negative variable constraints: -

X, Y >=0

Here, the constraints are production hours, skilled labour hours and material units and can be be expresses mathematically as: -

For production hours -

5X + 3Y <= 180 ....... equation (i)

For Skilled Labour Hours -

5X + 6Y <= 240 ....... equation (iI)

For material -

2X + 2Y <= 100

2(X + Y) <= 100

X + Y <= 50

Demand constraint

X >= 30

Y >= 10

Now, plotting equation (i) & (ii) and non negative constraint on graph and shading the region which satisfies the equation we get 4 different corner points and then using those corner points in maximizing equation we get our optimum product mix which is as under:

MV Cable = 0

LV Cable = 40

Maximum contribution = 40 X 350 = RO 14000

The graph and calculation of points on graph is attached.