1. A Company is trying to decide how many snow tires it should manufacture in its Detroit plant for the upcoming winter season.  Given the seasonal nature of the product the company will have to commit to the production plan 3 months prior to the start of the production so that the required materials can be purchased, and the labor force can be planned.  The set-up cost required for the production run is $20,000.  You are given the following data:

Selling price/tire during the winter season: $120

Variable Cost/tire:  $40

Any tire that is not sold by the end of the winter season will be sold to a discount retail store for $20.  Also, if demand for a snow tire cannot be met the company has decided to give a $38 discount/tire to be used against purchases next season. 

 The beginning inventory of snow tires is zero.  Demand is not known with certainty, but assumed to follow the following probability distribution.

           

Demand(units)	Probability
500	0.10
1000	0.20
1500	0.40
2000	0.15
2500	0.10
3000	0.05

          

1. What is the optimum production quantity?
2. What is the expected profit associated with the optimum production quantity?
3. For this part of the question assume that the GreatYear Tire Company has a beginning inventory of 1,500 snow tires. What is the optimum production quantity? Explain your answer. 
4. What would your answers to parts (a), (b) and (c) above be if the set-up cost was $10,000?