Q. 28

# A dealer wishes t

Let the dealer buy x fans and y sewing machines. The LPP is to maximize profit Z = 22x + 18y

Subject to constraints:

x + y ≤ 20

360x + 240y ≤ 5760

3x + 2y ≤ 48 and x ≥ 0, y ≥ 0

First we draw the lines AB and CD whose equations are x + y = 20

And 3x + 2y = 48

The feasible region is OBPCO which is shaded in the above figure.

P is the point of intersection of the lines x + y = 20 and 3x + 2y = 48.

Solving these equations, we get the point P (8, 12).

The vertices of the feasible region are O (0, 0), B (0, 20), P (8, 12), C (16, 0)

The value of objective function Z = 22x + 18y at these vertices are as follows:

The maximum profit is Rs. 392 when 8 fans and 12 sewing machines are purchased.

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