Final answer:
To maximize the profit function P = 3x + 2y, we need the graph or constraints that define the feasible region. Once we have those, we can calculate the profit at each corner point of the region. The point yielding the highest profit is the solution.
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 for a given graph and to find the maximum value. To solve this problem, we utilize a method similar to finding the point where total revenue exceeds total cost by the largest amount, which would tell us where the profit is maximized based on the provided data. In the context of profit functions and graphs in a perfectly competitive market, you would typically look at the profit curve or the data given to determine at which quantity profit is maximized. For the linear function P = 3x + 2y, the maximization occurs at the corner points of the feasible region defined by the graph's constraints. The objective is to evaluate the profit function at each of these corner points and choose the point which yields the highest profit value. After calculating this for all the given points, the one with the highest profit is the answer. Assume we were given specific points as part of our constraints, we would then plug each point into the profit function to determine which one provides the highest value of P.
For this particular case, calculating the profit at different output levels based on total cost and total revenue curves would require the detailed data points, which aren't provided here. However, as per the example of calculating profit between 70 and 80 where profit equals $90, we can relate that the quantity of output that provides the highest level of profit is where the difference between total revenue and total cost is the greatest, similar to choosing the point (x,y) that maximizes P = 3x + 2y.
Without the specific constraints or the graph, however, we cannot give a numerical answer to this particular question. If the student can provide the graph or the constraints that define the feasible region for the values of x and y, we can then apply the described procedure to find the solution.