Boutique Guitars and Gear carries several types of strings. For one type, each package of strings costs the store $3.50 to purchase, and the store can sell them for $6.50 a piece. He estimates that not having the strings in stock if someone wants them costs him about $0.50 in business goodwill. However, after 6 months the strings start to age and he has to drop the prices to $2.50 per pack to get them to sell. He estimates demand for the strings in the next 6 months using the table below. Generate a payoff table, and compute the expected value for each alternative. How many packs of strings should the guitar shop purchase?
Demand Probability
10 0.10
11 0.15
12 0.35
13 0.25
14 0.15