Question

To ensure a full line of outdoor clothing and accessories, the marketing department at Teddy Bower insists that they also sell waterproof hunting boots. Unfortunately, neither Teddy Bower nor TeddySports has expertise in manufacturing those kinds of boots. Therefore, Teddy Bower contacted several Taiwanese suppliers to request quotes. Due to competition, Teddy Bower knows that it cannot sell these boots for more than $54. However, $40 per boot was the best quote from the suppliers. In addition, Teddy Bower anticipates excess inventory will need to be sold off at a 50 percent discount at the end of the season. Given the $54 price, Teddy Bower’s demand forecast is for 300 boots, with a standard deviation of 200.

a. If Teddy Bower decides to include these boots in its assortment, how many boots should it order from its supplier? (Round your answer to nearest whole number.)

Number of boots should it order from its supplier is ___?

b. Suppose Teddy Bower orders 280 boots. What would its expected profit be? (Round your answer to the nearest whole number.)

Expected profit is ___?

c. John Briggs, a buyer in the procurement department, overheard at lunch a discussion of the “boot problem.” He suggested that Teddy Bower ask for a quantity discount from the supplier. After following up on his suggestion, the supplier responded that Teddy Bower could get a 10 percent discount if they were willing to order at least 600 boots. If the objective is to maximize expected profit, how many boots should it order given this new offer? (Enter your answer as a whole number.)

Number of boots should it order given the new offer is ____?

Answer 1

ANSWER:

Given that;

In the question,

\mu=300

\sigma=200

Price= $5

Costt=40

50% discount in the invenory

Cost of understocking Cu=54-40=$14

Cost of overstocking Co =40-54/2 =$13

Answer a= Critical ratio =Cu/(Cu+Co) = 14/(14+13) =0.5185

The corresponding z value for 0.5185 is 0.05

Z value = (Q-\mu)/\sigma

0.05 =(Q-300)/200

Q=300 boots

Answer= 300 boots

Answer b-

Expected lost sales =280-300/200 =-0.1

L(-0.1)=0.4349

Expected lost sales =0.4349*200 =86.98

Expected sales =300-86.98=213.02

Expected left over invenory=280-213.02=66.98

Expected profit =Sales revenue -Cost of expected left over inventory

Expected profit =14*213.02 -66.98*13

Expected profit =2111.5

Answer C= Here we have to compare the profit earned for 600 units

For 600 units=

Expected lost sales =600-300/200 =1.5

L(1.5)=0.0427

Expected lost sales =0.0427*200=8.54

Expected sales =300-8.54=291.46

Expected leftover invenory=600-291.46 =308.54

Expected profit =18*291.46 -308.54*9

Expected profit =2461.14

So the discount at 600 units is more

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