Find the optimal order quantity and optimal expected profit for probabilities of a harsh winter ranging from 0.2 to 0.8 in increments of 0.2. Plot optimal expected profit as a function of the probability of a harsh winter.

Midwestern Hardware must decide how many snow shovels to order for the coming snow season. Each shovel costs $ 15.00 and is sold for $ 29.95. No inventory is carried from one snow season to the next. Shovels unsold after Fabruary are sold at a discount price of $ 10.00. Past data indicate that sales are highly dependent on the severity of the winter season. Past seasons have been classified as mild or harsh, and the following distribution of regular price demand has been tabulated:

Shovels must be ordered from the manufacturer in lots of 200; thus, possible order sizes are 200, 400, 1,400, 1,600, 2,400, 2,600, and 3,000 units. Construct a decision tree to illustrate the components of the decision model, and find the optimal quantity for Midwestern to order if the forecast calls for a 40% chance of a harsh winter.

Mild Winter Harsh Winter No. of Probability No. of Probability Shovels 250 300 350 Shovels 0.5 0.4 0.1 1,500 0.2 2500 0.3 3,000 0.5