Tom owns an independent bookstore located in Philadelphia. Tom has to decide on the best order quantity for a new self-help book that is to be released soon. The books will each cost Tom $20 but will retail for $30. At the end of the season, Tom can dispose of all of the unsold copies of the book at $5 each. Tom estimates that demand can be represented by a normal distribution with mean 240 and a standard deviation of 100. The publisher’s cost per book is $7. a. What order quantity maximizes Tom’s expected profit? b. What is Tom’s expected profit? c. What is the resulting profit for the publisher?Now consider the supply chain to be a single (vertically-integrated) entity.d. What quantity will maximize the supply chain’s profit? e. How much is the total supply chain profit?The publisher is proposing a buy-back arrangement: At the end of the season, they will buy back all unsold copies at $15.00. However Tom is responsible for shipping unsold copies back to the publisher at $1 per book. f. What quantity should Tom order if he wishes to maximize his expected profit? g. What is the resulting profit for the publisher? h. What is the total profit for the supply chain?Consider the question of the best buy-back price.i. Compute the best buy-back price.j. Compute the resulting profit for Tom under the best buy-back price.k. Compute the resulting profit for the publisher under the best buy-back price.l. What is the total profit for the supply chain now?