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

a) Probability that the parka turns out to be a dog :

Standard normal deviate (99.5%) = Expected - Mean / S.D

= 0.5 * 2100 - 2100 / 1200 = -0.875

Look in the table of normal standard deviation probability corresponding to -0.875 is 0.1894 or 18.94%

b) Co = Overage cost = $22 - $10 = $12

Cu = Underage cost = $10 - 0 = $10

Critical ratio = Co / Co + Cu = 12/ 22 = 0.5455

From normal std.deviation z = 0.1143

Expected quantity to maximize profit = Mean + z * SD = 2100 + 0.1143 * 1200 = 2,237 units

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