You are an inventory specialist for Specialty Toys, Inc. The company sells a var

Question

You are an inventory specialist for Specialty Toys, Inc. The company sells a variety of new and innovative children’s toys. You know that the preholiday season is the best time to introduce a new toy because many families use this time to look for new ideas for December holiday gifts. When the company discovers a new toy with good market potential, it chooses an October market-entry date.

For you to get toys in your stores by October, you place one-time orders with manufacturers in June or July of each year. You are aware that demand for children’s toys can be highly volatile. If a new toy catches on, a sense of shortage in the marketplace often increases the demand to high levels and large profits can be realized. However, new toys can also flop, leaving the company stuck with high levels of inventory that must be sold at reduced prices.

The most important question you face is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If you order too few, sales will be lost; if you order too many, profits will be reduced because of low prices offered in clearance sales.

For the coming season, the company plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear will make weather predictions using an internal barometer when its hand is pressed. Tests show the toy’s weather predictions are quite good as compared to local television forecasters.

The sales department has given you the following sales forecast information:

1)What quantity would you need to order to have a 70% chance of meeting demand?

A) 30,000
B)17,447
C)22,653

The cost of goods sold for a Weather Teddy is $16. Your company sells the bears at a retail price of $24, for a profit of $8 per unit. However, any Teddys that are not sold during the holiday season are to be quickly sold at a clearance price of $5 for a loss of $11 per unit.

A common method for determining the order quantity is called the single-period inventory model. This model fits your current situation because you are making only one single order for the holiday season. The maximum expected profit in the single-inventory model is based on the following formula:

where P(Demand Q*) is the probability that demand is less than or equal to the recommended order quantity, Q*. The term cu is the cost per unit of underestimating demand (and losing sales because of going out of stock) and co is the cost per unit of overestimating demand (having unsold inventory). So,

cu = $24 - $16 = $8 lost per unit if Weather Teddy runs out of stock and

cu = $16 - $5 = $11 lost per unit if left-over inventory must be sold at the clearance price.

Therefore

2) What is the optimal production / order quantity in order to maximize profit?

A)17,273

B)18,980

C)21,024

Explanation / Answer

for mean =20000

and at 0.975 percentile z=1.96

hence std deviation =(30000-20000)/1.96=5102.04

also for 70 percentile z=0.52

hence corresponding value =mean+z*std deviation =20000+0.52*5102=22653

2)for 0.4211 percentile; z=-0.199

hence corresponding value =mean+z*std deviation =20000-0.199*5102=18980

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