Question

A manufacturer produces two different models – X and Y of the same product. Model X makes a 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 18 kg of r1 and 12 kg of r2 must be used daily. Also at most 34 hours of labour are to be utilized. A quantity of 2 kg of r1 is needed for model X and 1 kg of r1 for model Y. For each of X and Y, 1 kg of r2 is required. It takes 3 hours to manufacture model X and 2 hours to manufacture model Y. How many units of each model should be produced in order to maximize the profit.

Answer 1

Answer:

Let 'a' be the number of units of X model

Let 'b' be the number of units of Y model manufactured every day.

Total profit P = 50a +30b

The maximum value of profit = ?

First find the maximum value of a and b.

Maximum hours of labor available = 34 hours.

X takes 3 hours to manufacture a unit

Y takes 2 hours to manufacture a unit.

So Maximum hours of labor available/no of hours taken by X

= 34/3 = 11 units of X can be manufactured.

So Maximum hours of labor available/no of hours taken by Y

= 34/2 = 17 units of Y can be manufactured.

Substituting the above unit values in the equation for total profit

P = (50*11 + 30*17) = Rs. 1060

So to get maximum profit, we need to manufacture 11 units of Model X and 17 units of Model Y.