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 550 boots, with a standard deviation of 450.

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 530 boots. What would its expected profit be? (Round your answer to the nearest whole number.)

Expected profit it ___?

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 13 percent discount if they were willing to order at least 1,100 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 this new offer is ___?

Answer 1

Answer (a)

In the question,

=550

=450

Price= $54

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-)/

0.05 =(Q-550)/450

Q=572.5 boots

Answer= 572 boots

Answer (b)-

Expected lost sales =(530-550)/450 =-0.044

L(-0.044)=0.4139

Expected lost sales =0.4139*450 =186.255

Expected sales =550-186.255=363.745

Expected left over invenory=530-363.745=166.255

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

Expected profit =14*363.745 -11.5*13

Expected profit =&4942.93

Answer C= Here we have to compare the profit earned for 572 and 800 units

For 572 units=

Expected lost sales =(572-550)/450 =0.048 or 0.05

L(0.05)=0.3744

Expected lost sales =0.03744*450=16.848

Expected sales =550-16.84=533.16

Expected leftover invenory=572-533.16 =38.4

Expected profit =14*533.16 -38.4*123

Expected profit =2741.04$

For 1100 units=

Expected lost sales =1100-550/450 =.1.22

L(01.22)=0.0627

Expected lost sales =0.0627*450=28.215

Expected sales =550-16.848= 533.152

Expected leftover invenory=1100-533.152 =566.848

Expected profit =18*533.152 -566.848*9

Expected profit =4495.104$

So the discount at 1100 units is more

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