Question

A manufacturer produces two difierent models : X and Y, of the same product. Model X generates profit of Rs.50 per unit and model Y generates profit of Rs.30 per unit. 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 to maximize the profit?

Answer 1

Answer:

11 units of the X model and 17 units of the Y model should be produced to maximize the profit.

Step-by-step explanation:

Let us assume that 'a' units of the X model and 'b' units of the Y model are manufactured every day.

Hence, the total profit (P) =50a +30b ......(1)

So, to make the profit maximum a and b must be maximum.

Now, 3 hours is required for manufacturing one unit of X.

Hence, in at most 34 hours of labour, a maximum of 11 units of X can be manufactured.

Now, 2 hours is required for manufacturing one unit of Y.

Hence, in at most 34 hours of labour, a maximum of 17 units of Y can be manufactured.

In that case, from equation (1), maximum profit will be  

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

Therefore, 11 units of the X model and 17 units of the Y model should be produced to maximize the profit. (Answer)

Answer 2

11 units of X and 17 units of Y must be produced to get maximum profit.

Step-by-step explanation:

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

Then Total profit P = 50a +30b

We need to find maximum value of profit, hence we need to find maximum value of a and b in the above equation.

Maximum hours of labour available = 34 hours.

X takes 3 hours to manufacture a unit and Y takes 2 hours to manufacture a unit.

So 34/3 gives that 11 units of X can be manufactured.

So 34/2 gives that 17 units of Y can be manufactured.

Substituting the above unit values in the equation for total profit, we get P = (50*11 + 30*17) = Rs. 1060

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