Promus sells wireless routers. They need to decide how many routers to order (Q) from their suppliers. The routers cost $75 per unit and Promus sells the routers for $125 per unit. The total product cost is determined by the number of routers purchased and the product cost. Demand for the routers is distributed normally with a mean of 106 and a standard deviation of 19. Sales are the minimum of demand and order quantity. Revenue is determined by sales times the sales price. If Promus does not order enough routers, they incur a shortage cost equal to demand minus the order quantity, to capture the value of lost sales. Shortages cannot be negative. Shortage cost is shortages times the shortage cost per unit. Likewise, if Promus orders too many routers, they incur a holding cost of order quantity minus demand, to capture the cost of inventory. Holdings cannot be negative. Holding cost is holdings times the holding cost per unit. Product cost is the product cost per unit times the order quantity. Total cost is the sum of product cost, shortage cost, and holding cost. Profit is revenue minus total cost. Assume that Promus orders 130 routers.

(a) Calculate the total product cost.

(b) Create a random demand variable.

(c) Create a sales variable.

(d) Create shortage and shortage cost variables.

(e) Create holding and holding cost variables.

(f) Create a revenue variable.

(g) Create a total cost variable.

(h) Create a profit variable.

(i) What is the emperical probability that Promus will incur a shortage?

(j) Create a data table for the mean profit over the order quantities listed.

(k) Is 130 a reasonable order quantity, if Promus seeks to maximize expected profit? Why or why not?