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
quantityof2kgof r1isneededformodelXand1kgof r1formodelY.ForeachofX
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?
Answers
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 '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.
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