16.4.18 A Question Help 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 harsh winter. Click here to view the details of the scenario. Click here to view the decision tree. units for an expected profit of $ For P(harsh) = 0.2, the optimal order size is (Round to the nearest whole number as needed.) Details of the scenario Decision tree Each shovel costs $16.00 and is sold for $31.95. No inventory is carried from one snow season to the next. Shovels unsold after February are sold at a discount price of $9.00. 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: The decision tree starts with a decision node with seven branches, one for each order size. Each branch has the form shown. Mild Winter No. of Shovels Probability 250 0.4 300 0.3 350 0.3 Harsh Winter No. of Shovels Probability 1,500 0.2 2,500 0.4 3,000 0.4 Mild Demand 250 Demand 300 Demand 350 Demand 1,500 Demand 2.500 Demand 3.000 0.4 0.3 0.3 0.2 Order Size Harsh 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. 0.4 Print Done Print Done 16.4.18 A Question Help 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 harsh winter. Click here to view the details of the scenario. Click here to view the decision tree. units for an expected profit of $ For P(harsh) = 0.2, the optimal order size is (Round to the nearest whole number as needed.) Details of the scenario Decision tree Each shovel costs $16.00 and is sold for $31.95. No inventory is carried from one snow season to the next. Shovels unsold after February are sold at a discount price of $9.00. 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: The decision tree starts with a decision node with seven branches, one for each order size. Each branch has the form shown. Mild Winter No. of Shovels Probability 250 0.4 300 0.3 350 0.3 Harsh Winter No. of Shovels Probability 1,500 0.2 2,500 0.4 3,000 0.4 Mild Demand 250 Demand 300 Demand 350 Demand 1,500 Demand 2.500 Demand 3.000 0.4 0.3 0.3 0.2 Order Size Harsh 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. 0.4 Print Done Print Done