The manager of a firm estimates that the sales of her firm are related to radio and newspaper advertising in the following way: S = 12,000 + 1,800AR, where S = the number of units sold, A = the number of quarter-page newspaper advertisements, and R = the number of minutes of radio spots.

a. Derive the marginal benefit of newspaper and radio advertising. [Hint: The marginal benefit of advertising can be found by determining how much S changes for each one-unit change in A, holding R constant.] ?S/ ?A = __________ and ?S/?R=__________

b. If the newspaper ads cost $600 per quarter-page ad ( PA = $600 ) and the radio ads cost $200 per minute ( PR = $200 ), find the combination of radio and television ads that maximizes sales when the advertising budget is $7,200. Also compute the optimal level of sales. [Hint: Set MBA PA = MBR PR , then solve for either A or R and substitute this expression into the budget constraint 600A + 200R = $7,200 to solve for A* and R*.] A* = ________ R* = ________ S* = ________

c. Suppose the advertising budget is cut so that only $4,800 can be spent on advertising. Now what are the sales-maximizing values of A, R, and S ? A* = ________ R* = ________ S* = ________

d. Based on parts b and c, what is the effect of changing the advertising budget constraint on the optimal level of sales? ?S* / ?B= ________, where ?B is the change in the advertising budget. Do you expect this number to be positive or negative?