Green Mountain Sports [40 pts] Green Mountain Sports sells a full line of outdoor clothing and accessories, including waterproof hiking boots. Due to competition, Green mountain can sell these hiking boots for only $54 but must pay suppliers $40 per pair. One order is placed per season; excess inventory is sold at a 50% price discount at the end of the season. At $54, estimated demand over the season is 400 pairs of boots with standard deviation of 300.

Given the prices and costs, how many waterproof hiking boots should Green Mountain order to maximize its profit?

Suppose Green Mountain orders 380 pairs of boots. What would its expected fill rate be?

Suppose Green Mountain orders 380 pairs of boots. What would the expected profit be?

Suppose marketing is unhappy with the order quantity in part a. They argue that Green Mountain should maintain a high service level and insist that enough boots be ordered to have at least a 98% fill rate. What order size corresponds to a 98% fill rate for these boots?

What is Green Mountain's expected profit if it orders the amount calculated in part d?