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?

DemandProbability

100.10

110.15

120.35

130.25

140.15