A store is trying to determine how many jackets to order. Jackets are normally sold for $75. However, after the season is over, the price will first drop to $50 (discount 1), and then to $30 (discount 2). 

 

Demand for the full price jackets is believed to be anywhere between 3,000 and 10,000. In addition, demand at discounts 1 and 2 is assumed to be a multiple of 1 and 2 of a full-price demand, respectively. For example, if full-price demand is 3,000, then at $30 customers would be willing to buy 6,000 jackets.

 

The Store has a contract with the jacket manufacturer that specifies a penalty that a store has to pay if their stock fails to satisfy customer demand. The manufacturer charges store a $15 fee for every lost sale. For example, if demand is 3,030 but the order quantity was 3,000, the store will have to pay manufacturer $15*(3,030-3,000) = $450. 

 

Finally, the unit cost of jackets depends on the number ordered.

Unit Cost	From	Unit cost
	0	$48.00
	5000	$47.00
	10000	$46.00

 

1.How many jackets should the store order to maximize the expected profit? What if the store orders 3,000, 7,000 or 10,000 jackets?

2.Make a model assuming that demand is 3,000 and order quantity is 7,000. What is the total order cost?

3,Make a model assuming that demand is 3,000 and order quantity is 7,000. What is the total profit?

4.Make a model assuming that demand is 3,000 and order quantity is 10,000. What is the total profit?

5.Make a model assuming that demand is 3,500 and order quantity is 3,000. What is the total penalty?

6.Make a model assuming that demand is 3,500 and order quantity is 3,000. What is the total profit?

7.Set up a simulation that takes into account random demand. Trying 1,000 numbers for the uncertain input, which order quantity may result in a negative total profit?

 

8.Set up a simulation that takes into account random demand. Trying 1,000 numbers for the uncertain input, which order quantity results in a highest average total profit?

9.Set up a simulation that takes into account random demand. Trying 1,000 numbers for the uncertain input, which order quantity may results in an average total profit above $300,000?