Question

Solve A,B,C and please show work!!

PA 13-4 Fashionables is a franchisee of The Unlimited, the... Use Table 13.4 Fashionables is a franchisee of The Unlimited, the well-known retailer of fashionable clothing. Prior to the winter season, The Unlimited offers Fashionables the choice of five different colors of a particular sweater design. The sweaters are knit overseas by hand, and because of the lead times involved, Fashionables will need to order its assortment in advance of the selling season. As per the contracting terms offered by The Unlimited, Fashionables will also not be able to cancel, modify or reorder sweaters during the selling season. Demand for each color during the season is normally distributed with a mean of 450 and a standard deviation of 225. Further, you may assume that the demand for each sweater is independent of the demand for any other color. The Unlimited offers the sweaters to Fashionables at the wholesale price of $44 per sweater, and Fashionables plans to sell each sweater at the retail price of $70 per unit. The Unlimited does not accept any returns of unsold inventory. However, Fashionables can sell all of the unsold sweaters at the end of the season at the fire-sale price of $19 each. If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method How many units of each sweater-type should Fashionables order to maximize its expected profit? Use Table 13.4 and round to nearest integer a. If Fashionables wishes to ensure a 97.5% in-stock probability, what should its b. order quantity be for each type of sweater? Use Table 13.4 and round to nearest integer c. Say Fashionables orders 675 of each sweater. What is Fashionables' expected profit? Use Table 13.4.

Answer 1

Answer: Given: Cost of sweater = $44

Selling price = $70

Fire sale price = $19

Mean = 450

Std. Deviation = 225

a. EOQ:

We solve in excel as shown below:

Formulas R C $ $ $ S р Inputs Revenue per unit Cost per unit Salvage Value per unit Mean Demand Standard Deviation of Demand Cost of shortage Cost of Overage Service level Z-Score Number of Units per order 70.00 44.00 19.00 450 225 26.00 25.00 o $ $ Cu = R-C Co= C-S Cu/(CO + Cu) Z Q = u + Z* o 0.51 0.02 455.53

The above table in the form of formulas is shown below for better understanding and reference:

Inputs Formulas Revenue per unit R 70 Cost per unit |С 44 Salvage Value per unit S 19 Mean Demand μ 450 Standard Deviation of Demand o 225 Cost of shortage Cu = R-C =C2-C3 Cost of Overage Co= C-S =C3-C4 Service level Cu/ (Co + Cu) =C7/(C7+08) Z-Score Z =NORM.INV(C9,0,1) Number of Units per order Q = 4 + Z*0 =C5+(C10*С6)

EOQ = 456

Note: If this answer is not accepted, try either 450 or 473 as these are the answers obtained by rounding off Z score as per table 13.4

b) In stock probability = 97.5%

Z score = 1.96

$ $ $ 70.00 44.00 19.00 450 Inputs Formulas Revenue per unit R Cost per unit C Salvage Value per unit S Mean Demand μ Standard Deviation of Demand o Cost of shortage Cu = R-C Cost of Overage Co = C-S Service level Cu/ (CO + Cu) Z-Score Z Number of Units per order Q = u + Z* o $ $ 225 26.00 25.00 0.98 1.96 890.99

EOQ = 891

Note: If this answer is not accepted, try 900 as this is the answer obtained by rounding off Z score to Z=2 as per table 13.4

c. Order = 675 sweaters

Z =
Q 11 0
= $\frac{675-450}{225}$ = 1

From table 13.4, for Z = 1, l(z) = 1.0833

Expected inventory unsold = $1596257816445_blob.png$ * L(z) = 225 * 1.0833 = 243.74 = 244

Expected sale = Q - Expected inventory = unsold = 675 - 244 = 431

Total profit = Expected sale * (revenue - cost) - Unsold inventory (cost - salvage) = 431 * (70-44) - 244 (44-19) = 11,206 - 6100 = $5106 for 1 type of sweater

For 5 types of sweaters = $5106 * 5 = $25,530

Expected Profit = $25,530

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