Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

the feasible regions are three vertices are (0, 0), (8, 0), and (0, 8).

To find the minimum and maximum values of P,
evaluate P = 3x + 4y at each of the three vertices.

At (0, 0): P = 3(0) + 4(0) = 0 Minimum

At (8, 0): P = 3(8) + 4(0) = 24

At (0, 8): P= 3(0) + 4(8) = 32 Maximum

The minimum value of P is 0. It occurs when x = 0 and
y = 0. (0,0) The maximum value of P is 32. It occurs when
x = 0 and y = 8.

The minimum is P = at

(x, y) = (0,0)

.

The maximum is P = at

(x, y) = (0,8)

.

Please let me know if you need any clarification. I'm always happy to answer your questions.Please let me know if you need any clarification. I'm always happy to answer your questions.