Advertising Campaign

2-14. In the Ma-and-Pa grocery store, shelf space is limited and must be used effectively to

increase profit. Two cereal items, Grano and Wheatie, compete for a total shelf space of

60 ft2. A box of Grano occupies .2 ft2 and a box of Wheatie needs .4 ft2. The maximum

daily demands of Grano and Wheatie are 200 and 120 boxes, respectively. A box of

Grano nets $1.00 in profit and a box of Wheatie $1.35. Ma-and-Pa thinks that because

the unit profit of Wheatie is 35% higher than that of Grano, Wheatie should be allocated

35% more space than Grano, which amounts to allocating about 57% to Wheatie and

43% to Grano. What do you think?

2-17. Show & Sell can advertise its products on local radio and television (TV). The advertising

budget is limited to $10,000 a month. Each minute of radio advertising costs $15, and each

minute of TV commercials $300. Show & Sell likes to advertise on radio at least twice as

much as on TV. In the meantime, it is not practical to use more than 400 minutes of radio

advertising a month. From past experience, advertising on TV is estimated to be 25 times

as effective as on radio. Determine the optimum allocation of the budget to radio and TV

advertising.

2-19. Top Toys is planning a new radio and TV advertising campaign. A radio commercial costs

$300 and a TV ad costs $2000. A total budget of $20,000 is allocated to the campaign.

However, to ensure that each medium will have at least one radio commercial and one

TV ad, the most that can be allocated to either medium cannot exceed 80% of the total

budget. It is estimated that the first radio commercial will reach 5000 people, with each

additional commercial reaching only 2000 new ones. For TV, the first ad will reach 4500

people, and each additional ad an additional 3000. How should the budgeted amount be

allocated between radio and TV?