Chapter 4.1, Problem 44E

OPTIMIZING ADVERTISING EXPOSURE As part of a campaign to promote its annual clearance sale, Excelsior Company decided to buy television advertising time on Station KAOS. Excelsior's television advertising budget is $\$102,000$. Morning time costs $\$3000\text{/min}$, afternoon time costs $\$1000\text{/min}$, and evening (prime) time costs $\$12,000\text{/min}$ . Because of previous commitments, KAOS cannot offer Excelsior more than $6$ min of prime time or more than a total of $25\text{min}$ of advertising time over the $2$ weeks in which the commercials are to be run. KAOS estimates that morning commercials are seen by $200,000$ people, afternoon commercials are seen by $100,000$ people, and evening commercials are seen by $600,000$ people. How much morning, afternoon, and evening advertising time should Excelsior buy to maximize exposure of its commercials?