Problem:
A hotel chain is considering using yield management to increase profits. Its plan is to sell unsold rooms at a discounted rate very close to the night of stay. For example, an unsold Friday night room would be discounted early in the week. It estimates that the percentage of sold rooms (total) would be equal to 50+X, where X is the % discounted off of regular price. Meanwhile the % of rooms sold for full price compared to the discount would be 100-2X (some people would wait to book gambling a discount would happen).
Required:
Find the ideal discount %. Solve the problem and show all work.