Use table 13.4 to help fid answer please: TABLE 13.4 The Distribution, FIO), and

Question

Use table 13.4 to help fid answer please:

TABLE 13.4 The Distribution, FIO), and Expected Inventory, KO),Functions for a Normal Distribution with Mean 3000 and Standard Deviation 1000 Fla) F(a) 0455 0561 0686 0833 1004 1202 1429 1687 1978 2304 2668 3069 3509 3989 4509 5069 5668 6304 6978 7687 8429 9202 .4367 1.5293 16232 9332 1357 1587 1841 9452 0001 0001 0002 0002 0003 0005 9554 17183 9641 18143 1.9111 9772 2008s 2.1065 2.2049 2.3037 9918 2.4027 2.5020 99532.6015 2.7011 2.8008 2.9005 3.0004 3.1003 3.2002 3.3001 3.4001 3.5001 3.6000 3.7000 3.8000 3.9000 4.0000 0001 0001 0001 0002 0003 0004 9713 -0.7 2420 2743 3085 3446 3821 4207 4602 9821 9861 9893 0010 0013 0019 0026 0035 0047 9938 0008 0011 0015 0020 0027 0037 0049 9965 9974 9981 2.8 5398 5793 6179 6554 6915 7257 7580 7881 8159 3.0 9990 9993 9995 9997 9998 9998 0107 0139 3.2 .6 3.3 0228 0287 0359 0085 8 3.5 0143 0183 0232 0293 0367 1.0004 3.6 841310833 8643 1686 12561 .3455 0548 3.8 8849 3.9 1.0000 0808 9032 1.0000

Explanation / Answer

This is a case of classic newsvendor problem in which in need to make a decision of optimal ordering by balancing cost of over stocking and cost of understocking

Price of sweater = 68$

Cost of sweater = 42$

Profit = 26 $

Marginal cost with underestimation of demand = 26 $ (Cu)
Marginal cost by overestimating demand = 42-23 = 19 $ (Co)

Optimal occurs at a point when the expected benefit of an extra would be less than the expected cost for the item.
Expected marginal cost equation:
P(Co) (1-P)(Cu)

P <= Cu/(Cu+Co) = 26/(26+19)

P<=.58

As per table given Z score for P .58 ~ .2

Z = 0.2

Stock = Demand + Z* SD

= 425 + 225*.2 = 470

A. 470

B. If probability = 97.5

P value = 0.975

Z score ~ 1.96

Stock = 425 * 1.96*225 = 866 units

C & D.

If Order quantity = 650

650 = 425 + z* 225

Z= 1

Using normsdist formula in excel for z = 1

P = .8413

Stockout probability = 1- P = .158655 = 15.8655%

Expected lost sales = SD * P = 225*.158655 = 36 units

Expected sales = 425- expected lost sales = 425- 36 = 389 units

Expected profit = (profit* Expected sales) - (Overstock cost * Expected left over inventory )

Expected profit = 26* 389 - 19* (650-389) = 5,155$

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