CH 16 Decision Theory A hardware store must decide how many snow shovels to order for the coming snow season. Perform a sensitivity analysis and 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. Click here to view the details of the scenario. Click here to view the decision tree. For P(harsh) = 0.2, the optimal order size is units for an expected profit of $ (Round to the nearest whole number as nee - X 1,600 Details of the scenario 200 Each shovel costs $16.00 and is sold for $31.95. No inventory is carried from one 400 snow season to the next. Shovels unsold after February 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 2,400 following distribution of regular price demand has been tabulated: 1,400 Mild Winter Harsh Winter No. of Shovels Probability No. of Shovels Probability 250 0.4 1.500 0.1 2,600 300 0.5 2,500 0.4 - X 350 0.1 3.000 0.5 Decision tree 3,000 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. The decision tree starts with a decision node with seven branches, one for each order size. Each branch has the form shown. Demand 250 0.4 Print Done Mild Demand 300 0.5 Demand 350 Order Size 0.1 -O Demand 1,500 0.1 Harsh Demand 2,500 0.4 Demand 3,000 0.5