P2. Biscuits A restaurant sells biscuits for $1.5 each from 8:00am to 3:00pm. The biscuits are ordered from a supplier at the start of each day and delivered before the store opens. The supplier charges 75 cents per biscuit and there is no fixed ordering cost. If biscuits spend a night in storage they lose most of their taste and so if at 3:00pm some biscuits are left, the restaurant sells them off at 50 cents per biscuit. At that price, all "leftover" biscuits are sold (there is always enough demand at that price). The restaurant has estimated that if a customer demands a biscuit before 3:00pm but the restaurant has run out, besides losing the sale, this costs the restaurant $2.00 in loss of future sales. Moreover, demand for biscuits before 3:00pm usually varies between 40 and 45, with the probability of each demand scenario given in the following table. Demand before 3:00pm (biscuits) Probability (%) The table suggests that for 10% of days the demand before 3:00pm is 40 biscuits, for 15% of days the demand before 3:00pm is 41 biscuits, etc. The restaurant currently orders 42 biscuits every day. The goal of the problem is to advice the restaurant on how many biscuits to order on each day. (a) What is the expected number of demanded biscuits on a given day? What is the expected number of sales before 3:00pm given the current order size? How about the expected number of lost sales (units demanded but not available) before 3:00pm? What do you observe about those three quantities? (b) Assume that the number of demanded biscuits before 3:00pm on a given day is 41. How much would the restaurant regret not having ordered 41 biscuits instead of 42 (in %)? On the flip side, assume that the number of demanded biscuits before 3:00pm on a given day is 43. How much would the restaurant regret not having ordered 43 biscuits (in $) instead of 42? (c) Does the restaurant order too many or too few biscuits in your opinion? Why? (d) What is the right order size for the restaurant in your opinion