Problem 10-27 (Algorithmic) ly at a particular supermarket. The product, which c
ID: 383593 • Letter: P
Question
Problem 10-27 (Algorithmic) ly at a particular supermarket. The product, which costs $1.23 per unit, sells for $1.74 per unit. If units are unsold at the end of the day A perishable dairy product is ordered dail the supplier takes them back at a rebate of $1 per unit. Assume that daily demand is ap proximately normally distributed with -145 and = 25. Note: Use Appendix B to identify the areas for the standard normal distribution a. What is your recommended daily order quantity for the supermarket? Round your answer to the nearest whole number b. What is the probability that the supermarket will sell all the units it orders? Round your answer to three decimal places. . In problems such as these, why would the supplier offer a rebate as high as $17 For example, why not offer a nominal rebate of, say, 25 per unit? What happens to the ) supermarket order quantity as the rebate is reduced? the quantity that the supermarket should order decreasesExplanation / Answer
Cost of product = C = $ 1.23 / unit
Selling price of the product = P = $1.74 / unit
Salvage price = S = $1.23 - $1 ( rebate) = $0.23
Thus,
Underage cost = Cu = P – C = $1.74 - $1.23 = $0.51
Overage cost = Co = C – S = $1.23 - $0.23 = $1
Therefore,
Critical ratio = Cu/ (Cu + Co) = 0.51 / ( 0.51 + 1) = 0.51/1.51 = 0.3377
Thus probability of optimum order quantity = 0.3377
Corresponding Z value for probability 0.3377 = NORMSINV ( 0.3377) = - 0.4187
Thus daily optimum order quantity for the supermarket
= Mean demand + Zvalue x Standard deviation of demand
= 145 – 0.4187 x 25
= 145 – 10.4675
= 134.53 ( 135 rounded to nearest whole number )
Probability that supermarket will sell all it orders = 0.3377
DAILY OPTIMUM ORDER QUANTITY = 135
PROBABILITY THAT SUPERMARKET WILL SELL ALL IT ORDERS = 0.3377
Revised scenario under rebate of 25 cents per unit :
Cost of product = C = $ 1.23 / unit
Selling price of the product = P = $1.74 / unit
Salvage price = S = $1.23 - $0.25 ( rebate) = $0.98 / unit
Thus,
Underage cost = Cu = P – C = $1.74 - $1.23 = $0.51
Overage cost = Co = C – S = $1.23 - $0.98 = $0.25
Therefore,
Critical ratio = Cu/ (Cu + Co) = 0.51 / ( 0.51 + 0.25) = 0.51/0.76 = 0.6710
Thus probability of optimum order quantity = 0.6710
Corresponding Z value for probability 0.6710 = NORMSINV ( 0.6710) = 0.4426
The revised optimum order quantity for the supermarket
= Mean demand + Z value x Standard deviation of demand
= 145 + 0.4426 x 25
= 145 + 11.065
= 156.065 ( 156 rounded to nearest whole number )
Thus with reduction of rebate to $0.25 / unit , optimum order quantity increases from 135 to 156
THE HIGHER REBATE DECREASE THE QUANTITY SUERMARKET SHOULD ORDER
DAILY OPTIMUM ORDER QUANTITY = 135
PROBABILITY THAT SUPERMARKET WILL SELL ALL IT ORDERS = 0.3377
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