Answer to Question #244185 in Operations Research for Shormista2

Question

A manufacturer produces two different models -x and y of the same product.Model x makes contribution of Rs 50 per unit and model y Rs 30 per unit towards total profit.Raw materials r1 and r2 are required for production.At least 18kg of r1 and 12kg of r2 must be used daily.Also at most 34hours of labour are to be utilised.A quantity of 2kg of r1 is needed for model x and 1kg of r1 for model y.For each of X and Y 1kg of r2 is required.It takes 3 hours to manufacture model x and 2hrs to manufacture y. How many units should be produced to maximise the profit?

Answer 1

Solution:

Objective Function Max (Z)=50x + 30y,

Subject to constraints:

$2x + y \ge18 \\ x + y \ge12 \\ 3x + 2y \le34 \\ x, y \ge0$

Feasible region is ABC.

A(2,14), B(6,6),C(10,2)

Now, Z=50x + 30y

At A(2,14)

Z=520

At B(6,6)

Z=480

At C(10,2)

Z=560

So, maximum profit is 560 at C(10,2).

Thus, x=10, y=2.