Please provide full answers: Teddy Bower is an outdoor clothing and accessories

Question

Please provide full answers:

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of the order placement, demand is still uncertain: Teddy Bower forecasts that its demand is normally distributed with a mean of 2100 and a standard deviation of 1200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity (and also doesn’t collect a tax benefit for the donation).

a.

What is the probability this parka turns out to be a “dog,” defined as a product that sells less than half of the forecast?

b.

How many parkas should Teddy Bower buy from TeddySports to maximize expected profit?

a.

What is the probability this parka turns out to be a “dog,” defined as a product that sells less than half of the forecast?

b.

How many parkas should Teddy Bower buy from TeddySports to maximize expected profit?

Explanation / Answer

To be Calculated:

a) Probability of Parka turns out to be a “dog”

b) Quantities of Parka to maximise profit

Given Values:

Cost price of Parkas = $10

Selling price of Parkas = $22

Mean in Demand = 2100

Standard Deviation in Demand = 1200

Salvage value = 0

Solution:

a) Minimum units to be sold,

LSL = 2100/2 = 1050

Z (LSL) = [(LSL - Mean) / Standard Deviation]

Z (LSL) = [(1050 - 2100) / 1200]

Z (LSL) = [(-1050 / 1200]

Z (LSL) = -0.875 0r -0.88

From the Z-table, Probability at Z = -0.88 is;

P (Z=-0.88) = 0.1894 or 18.9%

The probability that the Parka will be a dog is 18.9%

b) Quantity of Parkas that should be ordered to maximise profit can be calculated as;

Overage cost, Co = Cost price - Salvage value

Co = 10 - 0

Co = $10

Underage cost, Cu = Selling price - Cost price

Cu = 22 - 10

Cu = $12

Critical ratio = Cu / (Co + Cu)

Critical ratio = 12 / (10+12) = 12 / 22 = 0.5455

From the Z-table, it can be observed that the closest Z-value for 0.5455,

Z = 0.12

Now, Z = (Quantity - Mean) / Standard Deviation

0.12 = (Q - 2100) / 1200

Q = (0.12 x 1200) + 2100

Q = 2244

Quantity of Parkas that should be ordered to maximise profit is 2244

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