A young entrepreneur has invented a new air-adjustable basketball shoe with pump, similar to those advertised widely by more expensive brand names. He contacted a supplier of Victor basketball shoes, a little-known brand with low advertising. This supplier would provide shoes at the nominal price of $6 per pair of shoes. He needs to know the best price at which to sell these shoes. As a business student with strong economics training, he remembered that the volume sold is affected by the product's price-the higher the price, the lower the volume. He asked his friends and acquaintances what they would pay for a premium pair of basketball shoes that were a "little off-brand." Based on this information, he developed the formula:
Volume = 1,000 - 20 Price
There are some minor expenses involved, including a $50 fee for selling shoes in the neighborhood (a fixed cost), as well as his purchase price of $6 per shoe. Develop an appropriate objective function and find the optimal price level using Solver.