TABLE 13.4The Distribution, F(Q), and Expected Inventory, I(Q), Functions for the Standard Normal DistributionFunctionF(z)(z)-4.0.0000.0000-3.9.0000.0000-3.8.0001.0000-3.7.0001.0000-3.6.0002.0000-3.5.0002.0001-3.4.0003.0001-3.3.0005.0001-3.2.0007.0002-3.1.0010.0003-3.0.0013.0004-2.9.0019.0005-2.8.0026.0008-2.7.0035.0011-2.6.0047.0015-2.5.0062.0020-2.4.0082.0027-2.3.0107.0037-2.2.0139.0049-2.1.0179.0065-2.0.0228.0085-1.9.0287.0111-1.8.0359.0143-1.7.0446.0183-1.6.0548.0232-1.5.0668.0293-1.4.0808.0367-1.3.0968.0455-1.2.1151.0561-1.1.1357.0686-1.0.1587.0833-0.9.1841.1004-0.8.21191202-0.7.2420.1429-0.6.2743.1687-0.5.3085.1978-0.4.3446.2304-0.3.3821.2668-0.2.4207.3069-0.1.46023509.0.5000.3989.1.53984509.2.5793.5069.3.6179.5668.4.6554.6304.5.6915.6978.6.7257.7687.77580.8429.8.7881.9202.9.81591.00041.0.84131.08331.1.86431.16861.2.88491.25611.3.90321.34551.4.91921.43671.5.93321.52931.6.94521.62321.7.95541.71831.8.96411.81431.9.97131.91112.0.97722.00852.1.98212.10652.2.98612.20492.3.98932.30372.4.99182.40272.5.99382.50202.6.99532.60152.7.99652.70112.8.99742.80082.9.99812.90053.0.99873.00043.1.99903.10033.2.99933.20023.3.99953.30013.4.99973.40013.5.99983.50013.6.99983.60003.7.99993.70003.8.99993.80003.91.00003.90004.01.00004.0000 PA 13-9 (Algo) CPG Bagels starts the day with a large production...CPG Bagels starts the day with a large production run of bagels. Throughout the morning, additional bagels are produced as needed.The last bake is completed at 3 p.m. and the store closes at 8 p.m. It costs approximately $0.25 in materials and labor to make a bagel.The price of a fresh bagel is $0.60. Bagels not sold by the end of the previous day are sold the next day as "day old" bagels in bags ofsix for $0.99 a bag. About two-thirds of the day-old bagels are sold; the remainder are just thrown away. There are many bagel flavors,but for simplicity, concentrate just on the plain bagels. The store manager predicts that demand for plain bagels from 3 p.m. untilclosing is normally distributed with a mean of 51 and a standard deviation of 25. Use Table 13.4.If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correctanswer will depend on using the specified method.How many bagels should the store have at 3 p.m. to maximize the store'sexpected profit (from sales between 3 p.m. until closing)? (Hint: Assume day-oldа.bagels are sold for $0.99/6 = $0.165 each, that is, don't worry about the fact thatday-old bagels are sold in bags of six.) Use Table 13.4 and round-up rule.(Round your answer to a whole number.)Suppose the store manager has 97 bagels at 3 p.m. How many bagels shouldb. the store manager expect to have at the end of the day? Use Table 13.4 andround-up rule.Suppose the manager would like to have a 0.99 in-stock probability on demandc. that occurs after 3 pm. How many bagels should the store have at 3 p.m. toensure that level of service? Use Table 13.4 and round-up rule.

A Small Introduction about Demand The request is a financial hypothesis that alludes to a shopper's craving to purchase items and administrations just as their status to take care of them. If all other conditions remain constant, a rise in the price of an item or service will reduce demand, and vice versa. Except in a few unusual circumstances, as the price of a thing rises, so does the demand for it. Let's pretend the product in question is a television set for the sake of this debate. If televisions are sold for the low price of $5 apiece, a huge number of people will buy them often. Most people would buy more televisions than they require, placing one in each room and maybe storing others in the attic.Solution: Selling price = $ 0.60 Cost = $ 0.25 The selling price of day-old bagels = 0.996= $0.165 Around 66% of day-old bagels are sold, so the successful selling cost of day-old bagels = 23×0.165 = $0.11 Mean demand, d = 51 The standard deviation of demand, s = 25 Under-stocking cost, Cu =Selling price - Cost = 0.60 -0.25 = $ 0.35 Over-stocking cost, Co = Cost - effective selling price of day-old bagels = 0.25 -0.11 = $ 0.14 Critical ratio= CuCu+Co = 0.350.35+0.14 = 0.7143 In Table 13.4, lookup for F(z) ≥ 0.7143, the closest value of F(z) in the table is 0.7257 Corresponding value of z = 0.6 (a): Number of bagels, the store should have at 3 pmd + z×s = 51 + 0.6×25 = 66 bagels (b): Number of bagels = 97 z = (97 -d)s = (97-51)25=1.84 The closest value of z is 1.8, Lookup for the corresponding value of I(z) in Table 13.4 I(z) = 1.8143 Expected number of bagels, store manager can expect to have at the end of the day = I(z)×s = 1.8143×25=45.4 46 bagels (rounded-up) (c): For 0.99 in-stock probability, Lookup for the value of F(z) closest to 0.99 in Table 13.4. The closest value of F(z) is 0.9893 The corresponding value of z = 2.3 Number of bagels, store should have at 3 pm = 51+2.3×25=108.5= 108.5 109 bagels (rounded-up)