CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. M.P.Keshari

Linear Programming

Q.12. A dealer wishes to purchase a number of fans and sewing machines. He has only Rs5,760 to invest and has space for at most 20 items. A fan cost him Rs360 and a sewing machine Rs240. He expects to sell a fan at a profit of Rs22 and a sewing machine at a profit of Rs18. Assuming that he can sell all the atoms that he buys, how should he invest his money to maximize the profit ? Solve graphically and find the maximum profit.

Solution :

Let x be the number of fans and y the number of sewing machines (bought and sold). According to the hypothesis , the linear programming problem is :
Maximize Z = 22 x + 18 y
Subject to the constraints as :
x + y ≤ 20 --------------------------- (1)
And 360 x + 240 y ≤ 5760
Or, 3x + 2y ≤ 48 --------------------------- (2)
And also x ≥ 0, y ≥ 0 --------------------------- (3)
Now the lines x + y = 20 and 3x + 2y = 48 is drawn.

Fig

The lines meet at E (8, 12). The feasible region is shaded. We see that the feasible region is bounded. The corner points are C (16, 0), E (8, 12) and B (0, 20).

Therefore, for maximum profit he should buy and sell 8 fans and 12 sewing machines. His maximum profit is Rs392. [Ans.]

Q.13. A man has Rs1,500 for purchasing rice and wheat. A bag of rice and a bag of wheat cost Rs180 and Rs120 respectively. He has the storage capacity of at most 10 bags. He earns a profit of Rs11 and Rs9 per bag of rice and wheat respectively. Formulate the above problem as an LPP to maximize the profit and solve it graphically.

Solution :

Do yourself.
[Ans. Max. Profit = Rs100, No. of rice bags = 5 = No. of wheat bags]

Paper By Mr. M.P.Keshari
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