Using The Function Provided, The Optimal Stocking Quantity Essay

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Problem 1
a. Using the function provided, the optimal stocking quantity, which maximizes expected profit, is approximately 584 newspapers. If 584 newspapers were to be ordered, Hamptonshire Express will net an expected profit of \$331.436 per day.
b. Using the Newsvendor Formula in Excel, or Q* = Norminv(Cu/(Cu+Co), Mean, Std Dev) and the values:
Cu = 1 - .2 = .8
Co = .2
Mean = 500
Std Dev = 100
Q* = 584.1621 or 584 newspapers. This verifies the quantity in part (a).
Problem 2
a. Based on the simulation, Anna can should invest 4 hours daily in the creation of the profile section. It provides the highest profit of \$371.33.
b. Marginal Cost = Marginal Benefit
10 = (.8*50)/(2*sqrt(h))
20sqrt(h) = 40
Sqrt(h) = 2
H = 4 hours, which verifies Sheen’s choice of effort in part (a).

Her effort is at the point where the marginal cost of spending the extra time to develop the profile section = marginal benefit of spending the extra time to develop the profile section; or the point where profit is maximized. If she spends the extra time to develop the profile section past where marginal cost = marginal benefit, she won’t be able to create enough demand for her newspaper, but if she spends less time than where marginal cost = marginal benefit, she won’t have a quality newspaper and misses out on additional sales, which leads to increased profits.
c. Comparison of the optimal profit with Problem 1 looks like this:
Stocking Quantity Daily Expected Profit
584 331.44
685 371.33

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