Final answer:
The maximum value of the profit function P = 3x + 2y is achieved when x = 5 and y = 0, resulting in a maximum profit of P = 15.
Step-by-step explanation:
The student is tasked with finding the values of x and y that maximize the objective profit function P = 3x + 2y, given a certain graph. To find the maximum value of this profit function, we must consider each of the provided ordered pairs (points on the graph) and substitute them into the profit function to see which gives the highest value of P.
Let's substitute the given points into the profit function:
- (0, 1): P = 3(0) + 2(1) = 2
- (0, 0): P = 3(0) + 2(0) = 0
- (3, 2): P = 3(3) + 2(2) = 9 + 4 = 13
- (5, 0): P = 3(5) + 2(0) = 15
After evaluating the profit function for each pair, we find that the point (5, 0) provides the highest profit, P = 15, which is the maximum value of the profit function. Hence, the maximum profit is when x = 5 and y = 0.