Question

Please please help me out!!!!!!!!!!!!!!

Answer 1

P = 34 is the maximum value

Explanation:

Sketch

x + y = 6

with x- intercept = (6, 0) and y- intercept = (0, 6)

2x + 3y = 16

with x- intercept = (8, 0) and y- intercept = (0,
`(16)/(3)`

Solve x + y = 6 and 2x + 3y = 16 to find intersection at (2, 4)

The feasible region has vertices at

(0,
`(16)/(3)`), (0, 0), 6, 0) and (2, 4)

Evaluate the objective function P = 5x + 6y at each vertex

(0, 0) can be rejected as it will not give a maximum

(0,
`(16)/(3)`) → 0 + 32 = 32

(6, 0) → P = 5(6) + 0 = 30

(2, 4) → P = (5(2) + 6(4) = 10 + 24 = 34 ← maximum value

Thus maximum value is P = 34 when x = 2 and y = 4