(Land’s End) Geoff Gullo owns a small firm that manufactures "Gullo Sunglasses." He has the opportunity to sell a particular seasonal model to Land’s End. Geoff offers Land’s End two purchasing options: ∙ Option 1. Geoff offers to set his price at $65 and agrees to credit Land’s End $53 for each unit Land’s End returns to Geoff at the end of the season (because those units did not sell). Since styles change each year, there is essentially no value in the returned merchandise. ∙ Option 2. Geoff offers a price of $55 for each unit, but returns are no longer accepted. In this case, Land’s End throws out unsold units at the end of the season. This season’s demand for this model will be normally distributed with mean of 200 and standard deviation of 125. Land’s End will sell those sunglasses for $100 each. Geoff ’s production cost is $25. a. How much would Land’s End buy if they chose option 1? [14.3] b. How much would Land’s End buy if they chose option 2? [14.3] c. Which option will Land’s End choose? [14.4] d. Suppose Land’s End chooses option 1 and orders 275 units. What is Geoff Gullo’s expected profit? [14.4]

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Answer:

Answer is explained in the explanation section below.

Explanation:

a)

Answer-a with option-1

the land end sale price is $100, purchase cost is $65 and salvege valu is $53

So the underage cost = Cu = 100-65 = 35 and overage cost = Co = 65-53 = 12

the critical ratio = Cu/(Cu+Co) = 35/47 = 0.7422

From the standard normal distribution function The Z value at 0.7422 = 0.66

The optimal order quantity = 200 + 0.66 x 125 = 282.5

The optimal order quantity = 282.5

b)

Answer-b with option-1

the land end sale price is $100, purchase cost is $55 and salvage value is $0

So the underage cost = Cu = 100-55 = 45 and overage cost = Co = 55-0 = 55

the critical ratio = Cu/(Cu+Co) = 45/100 = 0.45

From the standard normal distribution function The Z value at 0.45 = -0.12

the optimal order quantity = 200 - 0.12 x 125

The optimal order quantity = 185

c)

We have to calculate the expected profit in each case to determine which option Lands Ends should choose.

With option-1 Geoff's sells 282.5 units at $65 for total revenue of 18363 and production cost of 282.5 = 7063

Geoff credits Lands ends for each returned sunglass so we need to evaluate how many sunglasses Land Ends return.

Expected lost sales = 125 x 0.1528 = 19.1

Expected sales = 200 - 19.1 = 180.9

expected left over inventory = 282.5 - 180.9 = 101.6

Expected profit = (100-65) x 180.9 - (65-53)x 101.6 = 5112

Expected profit = 5112

Similarly with option 2 the Expected profit = 4053

So option-1 is preferred.

d)

If the Land chooses option-1 and orders 275 units Then Geoff earn = 275 x $65 = $17875

and production cost = $25 x 275 = $6875

With order quantity 275 the z statistics = 0.6

and expected lost sales = 125 x 0.6 = 21.09

Expected left over inventory = 275-200+21.09 = 96.09

So the Geoff's buy back cost = 96.09 x 53 = $5093

and expected profit = $17875 - $5093 = $5907

expected profit = $5907

(A)The optimal order quantity = 282.5

(B) The optimal order quantity = 185

(C) Expected profit = 4053

(D) Expected profit = $5907

What is Optical order quantity?

a) Answer-a with option-1

When the land end sale price is $100, the purchase cost is $65 and also the salvage value is $53

So the underage cost is = Cu = 100-65 = 35 and

overage cost is = Co = then is 65-53 = 12 the critical ratio = Cu/(Cu+Co) = 35/47 = 0.7422

From the quality Gaussian distribution function The Z value at 0.7422 is = 0.66

Then, The optimal order quantity is = 200 + 0.66 x 125 = 282.5

Thus, The optimal order quantity = 282.5

b) Answer-b with option-1

When the land end sale price is $100, the purchase cost is $55 and also the salvage value is $0

So the underage cost is = Cu = 100-55 = 45 and overage cost is = Co = 55-0 = 55

the critical ratio = Cu/(Cu + Co) = 45/100 = 0.45

From the quality Gaussian distribution function The Z value at 0.45 = -0.12

Then the optimal order quantity = 200 - 0.12 x 125

Thus, The optimal order quantity is = 185

c) Then We have to calculate the expected profit in each case to work out which option Lands Ends should choose.

With option-1 Geoff's sells 282.5 units at $65 for total revenue of 18363 and a cost of 282.5 = 7063

When Geoff credits Lands ends for every returned sunglass so we want to judge what number of sunglasses Land Ends returns.

Then the Expected lost sales is = 125 x 0.1528 = 19.1

After that Expected sales is = 200 - 19.1 = 180.9

Then expected left over inventory is = 282.5 - 180.9 = 101.6

After that Expected profit is = (100-65) x 180.9 - (65-53)x 101.6 = 5112

Thus, Expected profit is = 5112

Similarly, with option 2, the Expected profit is = 4053

So option-1 is preferred.

d) If the Land chooses option-1 and also orders 275 units Then Geoff earn = 275 x $65 = $17875 and also the cost is = $25 x 275 = $6875

With order quantity 275 the z statistics = 0.6 and also expected lost sales = 125 x 0.6 = 21.09

Then Expected left over inventory is = 275-200+21.09 = 96.09

So the Geoff's repurchase cost = 96.09 x 53 = $5093

and also expected profit is = $17875 - $5093 = $5907

Thus, Expected profit is = $5907

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