Find the maximum value of p=3x+2y subject to the following constraints:
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maximum value of P is 33

Step-by-step explanation:

Sketch the lines represented by the constraints

5x + y = 16

with intercepts (, 0) and (0, 16)

2x + 3y = 22

with intercepts (11, 0) and (0, )

The solutions to both are below the lines.

Solve 5x + y = 16 and 2x + 3y = 22 simultaneously to find the point of intersection at (2, 6)

The coordinates of the vertices of the feasible region are

(0, 0), (0, 16), (2, 6), 11, 0)

Evaluate the objective function at each vertex

P = 3(0) + 2(0) = 0 + 0 = 0

P = 3(0) + 2(16) = 0 + 32 = 32

P = 3(2) + 2(6) = 6 + 12 = 18

P = 3(11) + 2(0) = 33 + 0 = 33

The maximum value of P is 33 when x = 11 and y = 0