Innovative Sports sells a patented golf trainer called the Puttmaster. This device, which sells for $ 69.95, consists of a metal strip on the floor that is attached to the golfer’s putter with elastic bands. By taking practice strokes with the putter attached to the Puttmaster, the golfer learns to feel how the putt should be stroked.
The Puttmaster is sold through a distributor who sells to retail stores (golf shops and sports outlets) and to the public through infomercials. The distributor pays Innovative Sports $ 30.85 for each Puttmaster. Innovative Sports also sells them through 30- minute television infomercials and on the Golf Channel (a cable TV channel) for $ 69.95 plus $ 15.95 for shipping and handling. Although each infomercial increases the public awareness of the product, thereby stimulating sales in the retail stores, infomercial sales also preempt retail sales. The distributor sells sufficiently large numbers of units that, for every 10 Puttmasters sold via the infomercial, two units will not be sold in a retail outlet.
For each unit sold on the infomercial, Innovative Sports pays $ 5.80 to the shipping company for mailing and $ 2.00 to the phone-answering company for providing the toll- free number and processing the order. Innovative Sports purchases Puttmasters from the manufacturer, which produces them for $ 9.55. They are shipped directly to either the distributor or to the shipping company.
A 30- minute infomercial on the Golf Channel costs $ 845,000. Innovative Sports has already produced the taped show for the infomercial and is now deciding how many 30- minute infomercials to purchase over the next three months. The Golf Channel sells half- hour time slots 90 days in advance. From past experience, Innovative Sports estimates the first 30- minute infomercial will yield 22,000 unit sales. Each subsequent showing of the infomercial will yield only 90 percent of the units sold following the previous infomercial. How many 30- minute infomercials should Innovative Sports purchase for the next 90 days?