You are the buyer in the TV department of a local Best Buy and have to order a six month selling season's supply of a specific Toshiba 24 inch model one quarter (three months) ahead of the start of the six month selling season (e.g. you order the January to June season's TVs on the preceding October 1st.). Also, halfway through each selling season (e.g. on April 1st in the Spring season) Toshiba will immediately ship you a rush order of additional TVs for an extra $50 per TV more than the $200 per TV you pay on the initial order. Assume your forecast for the upcoming six month season predicts you will sell a mean of 200 TVs of this model with a standard deviation of 100, the retail price per TV is $325, the salvage value per TV is only $175 because TV models change every six months and that half way through the selling season you will know for certain exactly how many TVs you will sell in the second half of the season:
a) How many should you order on the first order (e.g. October 1st) to maximize profits?
b) How many TVs do you expect you will be ordering in your second order (e.g. April 1st)?