Question

Please help me out with this please

Answer 1

Answer:

P = 9 is the max value

Step-by-step explanation:

Sketch

2x + 4y = 10

with x- intercept = (5, 0) and y- intercept (0, 2.5)

x + 9y = 12

with x- intercept = (12, 0) and y- intercept = (0, $\frac{4}{3}$ )

Solve

2x + 4y = 10 and x + 9y = 12 to find the point of intersection at (3, 1)

The region corresponding to the solution of the system of constraints

Has vertices at (0, $\frac{4}{3}$), (0, 0) , (5, 0) and (3, 1)

Now evaluate the objective function at each vertex.

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

(5, 0) → P = 5 + 0 = 5

(0, $\frac{4}{3}$) → 0 + 8 = 8

(3, 1) → 3 + 6(1) = 3 + 6 = 9 ← maximum value

Thus the maximum value is 9 when x = 3 and y = 1