(a) A shopkeeper has to decide how may loaves of bread he should stock every week. The quantity of bread demanded in any week is assumed to be a continuous random variable, with a given probability function f (x). Let A be the unit cost of purchasing the bread, B the unit sale price, C the refund on unit sale of bread, and D the unit penalty cost. Find the optimum quantity of bread to be stocked.

(b) If A = 8, B = 20, C = 2 and D = 5, and the demand is regular between 1,000 and 2,000, show that the the optimum quantity is approximately 1,739 loaves of bread.