Frank owns a hot-dog stand. It costs him$1 to make each hot dog and he faces a linear price-response functiond(p) = (100-8p)+for each day.

1. Find Frank's contribution-maximizing price and the corresponding contribution. (For this and following questions, allow non-integer units of sales for simplicity.)
2. Suppose a big hot-dog franchise offers him a contract. According to the contract, the franchise will provide an unlimited number of prepared hot dogs per day for a fixed cost ofKdollars per day. If Frank accepts this contract, what is his optimal price?
3. For what values ofKshould Frank accept the contract if he is maximizing profit?

4. Now the franchise offers Frank a new contract that charges a daily fixed cost of$25. However, they will provide at most 40 hot dogs to Frank every day. Should Frank accept this offer? Explain your answer.