(20 points): Jaelyns Paddle Boards rents paddle boards. The store only operates from June 1 to Sept. 1 each year. Each paddle board rental is for 1 day.

Daily demand for paddle boards depends on how much wildlife is visible, which changes year to year. Historically, 50% of summers have been Good summers with lots of visible wildlife, 50% have been Bad summers with only a little bit of visible wildlife.

Historically, in a Good Summer, there is more demand for paddle board rentals than in Bad summers. Specifically, demand is given by:

Good Summer Demand DGood(p) = 50 - 0.5 * p

Bad Summer Demand DBad(p) = 25 - 0.75 * p

Thankfully, Jaelyn can tell by May 15 (before summer starts) whether the upcoming summer will be Good or Bad, so she can react and set prices appropriately. (Prices can change each year.)

Jaelyn currently has 15 paddle boards that she can rent out each day.

1. a) (5points)SupposeonMay15,sherealizesitwillbeaBadsummer.Whatpriceshould Jaelyn set for daily rentals this year to maximize her revenue? How many paddle boards does she expect to rent each day, on average? What will be her expected daily revenue?

2. b) (5 points) Suppose on May 15, she realizes it will be a Good summer. What price should she set for daily rentals this year to maximize your revenue? How many paddle boards does she expect to rent each day? What will be her expected revenue?

Jaelyns friend, Zayd, makes an offer to lease Jaelyn 20 additional paddle boards (bringing her total to 20 + 15 = 35) each day of the summer for the price of $80 per day. However, if Jaelyn wants this offer, she must decide by May 1st (no refunds).

c) (5 points) If Jaelyn had the additional 20 paddle boards (35 total), what price should she set if she assumed it would be a Good summer? What is her expected daily revenue and profit?

d) (3 points) Should Jaelyn accept Zayds offer? You can assume that Jaelyn has no additional costs if she does not take his offer. Be sure to justify quantitatively. (Hint: It may help to draw a decision-tree and leverage your answers to parts (a)-(c) for example, for a Bad summer, use the answer you came up with in part (a). You do not need to include the tree in your response but be sure to include any calculations not already show above.)