Andrew Evans, Inc., produces and sells toys for babies and toddlers, and the firm has enjoyed considerable success in the past few years as the post-World War II "baby boomers have made their own baby boom in the 1980s. Sales nationwide edged past the $4 million mark last year, and this year the president of Andrew Evans has set aside $1 million for advertising, up from $750,000 last year. The firm sells a variety of products, but it is a sufficient approximation to think in terms of an “average” product with an average price of $16 and marginal cost constant at $8 per “average” unit. The firm’s overheads are $800,000 per annum, excluding advertising.

Market research has culminated in the following estimate of the firm’s sales-advertising function:

Q = 110,386.3 + 298.674A - 0.10537A2 where Q represents the units of the “average” product, and A represents thousands of dollars spent on advertising.

(a) Calculate the expected sales volume and total profit given an advertising budget of $1 mil¬ lion.

(b) Calculate the profit-maximizing level of advertising expenditure.

(c) At that level, what would sales volume, revenue, and profit be?

(d) What reasons can you think of for supporting the president’s decision to spend $1 million on advertising?