Response to the following problem:
Frank's Garden Center sells McMurray riding mowers. McMurray has found itself with an excess inventory of Model 412 mowers and is temporarily offering dealers a discount of $75 off its normal wholesale price of $725. Frank's sells the Model 412 at a retail price of $895 and estimates that its demand during the upcoming selling season will be between one and five units, with the following probabilities:
P(Demand = 1 unit) = .25
P(Demand = 2 units) = .20
P(Demand = 3 units) = .10
P(Demand = 4 units) = .30
P(Demand = 5 units) = .15
Unfortunately, Frank's must decide how many mowers to purchase at the temporary price discount before the selling season begins. Once the selling season starts, if demand for the McMurray mower at Frank's exceeds the number ordered at the discounted price, Frank's must pay the normal wholesale price of $725 per unit. Any purchased mowers that Frank's is not able to sell during the normal selling season can be sold for $595 at the annual clearance sale.
How many mowers should Frank's purchase from McMurray at the temporary price discount?