A soft-drink producer must decide how to divide its spending between two forms of media: television advertising and magazine advertising. Each 30-second commercial on prime-time network television costs $120,000 and, by the company's estimate, will reach 10,000 viewers, 5,000 of whom are in the prime consumer age group, 15 to 25. A single-page ad in a leading human interest weekly magazine costs $40,000 and reaches 5,000 individuals, 1,000 of whom are in the 15 to 25 age group. In addition, the company plans to hold a sweepstakes contest to promote its new soft drink. (A requirement for entry is to enclose the coded label from the new drink.) The company believes the print ad will be more effective in generating trial purchases and entries. Each magazine spot is expected to produce 500 entries and each television spot 250 entries.
Finally, the company's goal in its promotion campaign is to reach at least 600,000 total viewers and 150,000 young viewers and to produce 30,000 or more contest entrants.
How many spots of each kind should it purchase to meet these three goals and do so at minimum cost?