Case :
JL Foods is planning to increase its advertising campaign front $1.4 million to $2 million based, in part, on the introduction of a new product. JL Taco $auce, to accompany its traditional products, JL Ketchup and JL Spaghetti Sauce. Tn the past, JL Foods promoted its two products individually, splitting its advertising budget equally between ketchup and spaghetti sauce. From past experience, the marketing department estimates that each dollar spent advertising only ketchup increases ketchup sales by four bottles and each dollar spent advertising only spaghetti sauce increases its sales by 3.2 bottles. $ince JL makes $0.30 per bottle of ketchup and $0.35 per bottle of spaghetti sauce sold (excluding the sunk cost of the given advertising budget), this amounts to a return of $1.20 (=4 X $0.30) per advertising dollar on ketchup and $1. 12 (=3.2 X $0.35) per advertising dollar on spaghetti sauce. Because taco sauce is a new product, its initial return is projected to be only $0. 1 0 per bottle, but each advertising dollar spent solely on taco sauce is estimated to increase sales by 11 bottles. The company also projects that sales of each product would increase by another 1.4 bottles for each dollar spent on joint advertising of the three products. JL wishes to maximize its increase in profits this year from advertising while also "building for the future" by adhering to the following guidelines for this year's advertising spending:
• A maximum of $2 million total advertising
• At most $400,000 on joint advertising
• At least $100,000 on joint advertising
• At least $1 million promoting taco sauce, either individually or through joint advertising
• At least $250,000 promoting ketchup only
• At least $250,000 promoting spaghetti sauce only
• At least $750,000 promoting taco sauce only
• At least as much spent this year as last year promoting' ketchup, either individually or by joint advertising
• At least as much spent this year as last year promoting spaghetti sauce, either individually or by joint advertising
• At least 7.5 million total bottles of product sold
a. Determine the optimal allocation of advertising dollars among the four advertising possibilities (advertising for each product individually and joint advertising). Give the total return per advertising dollar of this solution and express this as a percentage of the $2 million advertising budget.
b. What is the return on additional advertising dollars?
c. Suppose the constraint requiring that at least $750,000 be spent promoting only taco sauce were lowered to $700,000. How much would the profit increase?