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.