Meghan Alexandra Perfumes, Inc., manufactures a product line of exotic perfumes which are marketed worldwide. Sales of this perfume have been very strong, approaching a quarter of a million ounces in each of the first two years. Based on quarterly sales and advertising data Meghan has estimated the dependence of sales volume on advertising expenditures as follows:

Q = 52,833.98 + 248.358A - 0.049M2 where Q is ounces of the perfume, and A represents thousands of dollars spent annually on advertising. For the current year the advertising budget has been set at $950,000, over the objec¬ tions of the marketing vice-president, who feels that it should be substantially higher than that. Meanwhile, others in the strategy group claim that it is already too high and simply wasteful. The wholesale price of the perfume is $9.99, and the marginal cost of production is constant at precisely one-third of that. Overheads allocated to this product amount to $400,000 per annum, not including the advertising expenditure.

(a) At the planned level of advertising, and given the same price and cost situation, what will be the quantity demanded and the total profit for this line of perfumes?

(b) What is the profit-maximizing level of advertising expenditures?

(c) Is there a significant gain in revenues and profits available by adjusting advertising expendi¬ tures to a higher level?

(d) What assumptions and qualifications underlie your answers?