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
