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in Mathematics by (52.5k points)

Solve the LPP

Maximize Z = 30x + 25y

Subjected to 3x + 3y ≤ 18

and 3x + 2y ≤ 15, x, y ≥ 0

1 Answer

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Best answer

First, we draw the lines

3x + 3y = 18           ...(1)

and 3x + 2y = 15         ...(2)

The shaded region OCPB is the feasible region.

The vertices of the feasible region are C (5, 0), P (3, 3), B (0, 6) and O (0, 0)

By solving (1) & (2) we get co-ordinate of corner.

The value of z = 30x + 25y at the corner points are as :

z = 30x + 25y

At O (0, 0), Z = 30 × 0 + 25 × 0 = 0

At P (3, 3), Z = 30 × 3 + 25 × 3 = 90 + 75 = 165

At C (5, 0) Z = 30 × 5 + 25 × 0 = 150

At B (0, 6), Z = 30 × 0 + 25 × 6 = 150

Clearly maximum Z is 165 at (3, 3) i.e. when x = 3 and y = 3

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