XYZ Warehouse stocks 7 window air conditioner units for the coming week ...

XYZ Warehouse stocks 7 window air conditioner units for the coming week. No orders for additional air conditioners will be made until next week. The weekly consumer demand for window air conditioner units has the probability distribution as shown in the table below. Assume that a special stockout order is required each time there is a demand and no unit is available in stock. Assume XYZ Warehouse makes a $60 profit on each air conditioner sold from the weekly available stock. When a unit is sold as a special stockout order, XYZ Warehouse incurs an additional $80 cost resulting in a net loss of $20 for each unit sold on a special stockout order. XYZ Warehouse incurs a $10 inventory cost for any air conditioner unit not sold at the end of the week.

a) Find the expected profit for the week for window air conditioners.

b) How many air conditioner units should XYZ Warehouse have in stock at the beginning of a week to maximize expected profit?