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.Details of the scenario Each shovel costs $13.00 and is sold for $25.95. No inventory is mrried from one snow season to the next Shovels unsold after February are sold at a discount price or $10.00. Past data indicate that sales are highly dependent on the severity of the winter season. Past seasons have been classied as mild or harsh, and the following distribution of regular price demand has been tabulated: Mild Winter Harsh \"Enter '3. No. of Shovels Probability No. of Shovels Probability 250 0.4 1.500 0.1 300 0.4 2.500 0.2 350 0.2 3.000 0.? 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. Decision tree The decision tree starts With a decision node With seven branches. one 10f each order size. Each branch has the form shown. Demand 250 0.4 For P(harsh) =0.2, the optimal order size is units for an expected profit of $ (Round to the nearest whole number as nee For P(harsh) = 0.4, the optimal order size is an expected profit of $ (Round to the nearest whole number as nee 2 400 For P(harsh) =0.6, the optimal order size is 200 in expected profit of $ (Round to the nearest whole number as nee 400 For P(harsh) =0.8, the optimal order size is an expected profit of $ (Round to the nearest whole number as nee 2.600 Choose the correct graph below. 3,000 O A. OC. Profit 1.600 A Profit 30,000 30.000- 1.400