Question

30 POINTS

pl3. Find the values of x and y that maximize the objective profit function
P=3x+2y for the graph. What is the maximum value? Please show your work
-2
(0,1)
(0,0)
2
(3,2)
(5,0)

Answer 1

The maximum value of the profit function P = 3x + 2y is achieved at the point (5, 0), resulting in a profit of P = 15. Hence, the values x = 5 and y = 0 maximize the profit.

Step-by-step explanation:

The student has asked to find the values of x and y that maximize the objective profit function P = 3x + 2y. To solve this problem, we need to determine which point (x, y) among the given options will yield the highest value for P when substituted into the function.

1. For the point (0, 1), P = 3(0) + 2(1) = 2.
2. For the point (0, 0), P = 3(0) + 2(0) = 0.
3. For the point (3, 2), P = 3(3) + 2(2) = 9 + 4 = 13.
4. For the point (5, 0), P = 3(5) + 2(0) = 15.

The maximum value of P is obtained at the point (5, 0), which gives P = 15. This is the highest value of the profit function based on the given options, and thus, x = 5 and y = 0 are the values that maximize the objective profit function.