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

a. Find Frank’s contribution-maximizing price and the corresponding contribution.

(For this and following questions, allow non-integer units of sales for simplicity.)

b. 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 of K dollars per day. If Frank accepts this contract, what is his optimal price?

c. For what values of K should Frank accept the contract if he is maximizing profit?

d. 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.