An owner of a local basketball team has determined the following relationship between winning (w), total revenue (TR) and total cost (TC):

TR = 40w - 0.4w2

TC = 20 + 8w

Where w is the percent of its games the team wins.

a. Assuming the owner is a profit maximizer, determine the value for w that maximizes her profits. What are the resulting profits? (hint: you need to find MR and MC for wins and then employ the profit-maximizing rule of MR = MC). Sketch the result with a graph that has TR and TC on the vertical axis and w on the horizontal (like the graph we saw in class).

b. Suppose the team is taken over by a new owner who wants to maximize the team's winning percentage, subject to profits being greater than or equal to zero. What win percentage would she choose? Add this result to your earlier graph.

Answer rating: 100% (QA)

a To maximize profits MR TRw 40 08w MC TCw 8 Set MR MC 40 08w 8 08w 32 w 40 TR at ... View the full answer