Please help me with this question. All the answers provided in Chegg for this qu

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Please help me with this question. All the answers provided in Chegg for this question is wrong.

TABLE 13.4 The Distribution, F(O), and Expected Inventory, (), Functions for the Standard Normal Distribution Function Fiz) 0455 1.4367 1.5293 1.6232 1.7183 1.8143 0968 9332 9452 9554 0686 1587 0833 1841 0002 0002 0003 -0.9 -0.8 -0.7 -0.6 1202 1429 1687 1978 2304 2668 3069 3509 3989 4509 5069 5668 6304 6978 7687 8429 9202 9713 9772 9821 2420 2743 3085 3446 3821 4207 4602 5000 5398 5793 6179 6554 6915 7257 7580 7881 8159 8413 8643 8849 9032 2.0085 2.1065 0007 0002 2.2 2.3037 2.4027 2.5020 2.6015 2.7011 2.8008 2.9005 3.0004 3.1003 3.2002 3.3001 3.4001 3.5001 9893 9918 9938 9953 9965 9974 0003 0013 0019 0026 0035 0047 0062 0082 0107 -0.1 .0 .0015 0020 0027 0037 0049 0065 0085 .2 9987 9990 9993 9995 9997 9998 9998 .3 .5 0179 0228 0287 0359 0446 0548 0668 0143 0183 0232 0293 0367 9 1.0833 1.1686 1.2561 1.3455 3.8000 3.9000

Explanation / Answer

a)

Selling price, p = 45

Mfg cost, c = 8

Salvage value, v = 3

Underage cost, Cu = s - c = 45 - 8 = 37

Overage cost, Co = c - v = 8 - 3 = 5

Optimal service level F(z) = Cu/(Cu+Co) = 37/(37+5) = 0.8810

Look for F(z) equal to or greater than 0.8810 in Table 13.4, corresponding z value = 1.2 (for F(z) = 0.8849 )

Mean demand, µ = 300,000

Std dev of demand, = 100,000

Kilograms of Seed Monsanto should store in the warehouse, Q* = µ + z* = 300000 + 1.2*100000 = 420,000 kg

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b) given Q = 400,000

z value = (Q - µ)/ = (400000 - 300000)/100000 = 1

Look for z equal to or greater than 1 in Table 13.4, corresponding I(z) = 1.0833

Expected inventory, I(Q) = *I(z) = 100000*1.0833 = 108,330

Expected Sales, S(Q) = Q - I(Q) = 400000 - 108330 = 291670

Expected Revenue = S(Q)*p + I(Q)*v = 291670*45 + 108330*3 = $ 13,450,140

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c) Target in-stock probability, F(z) = 1 - stockout probability = 1-10% = 90%

Look for F(z) equal to or greater than 0.90 in Table 13.4, corresponding I(z) = 1.3 (for F(Z) = 0.9032)

Kilograms of seed Monsanto should place in the warehouse, Q =  µ + z* = 300000 + 1.3*100000 = 430,000

_______________________

d. Maximum profit for this seed = µ*Cu = 300000*37 = $ 11,100,000

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