Morty$$s Raincoats sells the Executive, a raincoat so popular that the demand is fairly steady

throughout the year $($during summer months, Morty exports them to the southern hemisphere$).$

The demand is $4000$ raincoats per year. Morty buys these raincoats for $$50$ per unit and stores

them in his basement. Morty$$s calculations show him that he generally incurs an opportunity

cost $($or cost of capital$)$ of $20\%$ per year on the value invested in inventory. Cost of

transportation is $$100/$order; in addition, Morty tips the truck driver $$25$ for every delivered order.

Assume $50$ weeks in a year.

a$.$ How many executives should Morty order every time he places an order?

b$.$ It is also known that the coats are actually made in Guadalajara, Mexico and it takes a

full week for a batch to be delivered after an order is placed. Given this information, what

is the optimal reorder point?