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

Linear Programming

Q.14. A factory owner purchases two types of machines, A and B for his factory. The requirements and the limitations for the machines are as follows:

He has maximum area of 9000 m2 available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximize the daily output?

Solution :

Let number of machines of type A be x and of type B be y.
Maximum daily output
z = 60x + 40y
subject to constraints
1000 x + 1200 y ≤ 9000
12 x + 8 y ≤ 72
x, y ≥ 0
Now, lines 1000 x + 1200 = 9000 => 5x + 6y = 45
And 12 x + 8y = 72 => 3x + 2y = 18 are drawn on the same graph paper as shown below which intersect at (9/4, 45/8).

Fig.

The corner points of the shaded region are O(0, 0), A(0, 7.5), B(9/4, 45/8) and C(6, 0).

The maximum output is at B and C. But the number of machines cannot be a fraction. Hence no. of machines of type A = 6 and no. of machines of type B = 0 [Ans.]

Paper By Mr. M.P.Keshari
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