HamptonshireEpxress Problems 1-3
Problem #1
A. How many newspapers should Sheen stock? Use the simulation in the spreadsheet
“Hamptonshire Express: Problem #1” to identify the optimal stocking quantity. What is the profit at this stocking quantity?
Optimal Stocking Quantity: 584
Expected profit at Optimal Stocking Quantity: $331.43
B. Verify that the value derived in part (a) is consistent with the optimal stocking quantity in the
Newsvendor model = mean = 500 = Standard Deviation = 100 = Overage Cost = $0.20‐$0 = $0.20 = Shortage Cost = $0.20‐$1.00 = ‐$0.80
= 1‐.8 = .2 corresponding z‐value = .84
.
∗
Problem #2
A. How many hours should Sheen invest daily in the creation of the profile section? The optimal amount of hours Sheen should invest results in optimal profit/day at: 4 hours
With optimal stocking quantity: 685
And expected profit/day: $371.33 B. What explains Sheen’s choice of effort level h? Since the marginal cost of her effort is $10/hour and the marginal benefit of her effort is equal to: .8 * 50 = 10 h = 4
2√
The hours invested will be optimized when marginal cost = marginal benefit, in this case h = 4.
C. Compare the optimal profit under this scenario with the optimal profit derived in Problem #1. Optimal Profit in #1 = $331.43 @ 584 units = $0.5675/unit
Optimal Profit in #2 = $371.33 @ 685 units = $0.5421/unit Although the optimal profit is increased from scenario 1 to scenario 2 by $39.90 the per unit profit is down by 0.0254/unit produced, however since overall profit is up, the added hours invested is still optimal. Problem #3
A. Assuming h=4 what would Armentrout’s stocking quantity be? Armentrout’s optimal stocking quantity is 516 B. Why does the optimal stocking quantity differ from the optimal stocking quantity identify in
Problem #2? Is the result here consistent with the newsvendor formula?
The optimal stocking quantities differ because there
A. How many newspapers should Sheen stock? Use the simulation in the spreadsheet
“Hamptonshire Express: Problem #1” to identify the optimal stocking quantity. What is the profit at this stocking quantity?
Optimal Stocking Quantity: 584
Expected profit at Optimal Stocking Quantity: $331.43
B. Verify that the value derived in part (a) is consistent with the optimal stocking quantity in the
Newsvendor model = mean = 500 = Standard Deviation = 100 = Overage Cost = $0.20‐$0 = $0.20 = Shortage Cost = $0.20‐$1.00 = ‐$0.80
= 1‐.8 = .2 corresponding z‐value = .84
.
∗
Problem #2
A. How many hours should Sheen invest daily in the creation of the profile section? The optimal amount of hours Sheen should invest results in optimal profit/day at: 4 hours
With optimal stocking quantity: 685
And expected profit/day: $371.33 B. What explains Sheen’s choice of effort level h? Since the marginal cost of her effort is $10/hour and the marginal benefit of her effort is equal to: .8 * 50 = 10 h = 4
2√
The hours invested will be optimized when marginal cost = marginal benefit, in this case h = 4.
C. Compare the optimal profit under this scenario with the optimal profit derived in Problem #1. Optimal Profit in #1 = $331.43 @ 584 units = $0.5675/unit
Optimal Profit in #2 = $371.33 @ 685 units = $0.5421/unit Although the optimal profit is increased from scenario 1 to scenario 2 by $39.90 the per unit profit is down by 0.0254/unit produced, however since overall profit is up, the added hours invested is still optimal. Problem #3
A. Assuming h=4 what would Armentrout’s stocking quantity be? Armentrout’s optimal stocking quantity is 516 B. Why does the optimal stocking quantity differ from the optimal stocking quantity identify in
Problem #2? Is the result here consistent with the newsvendor formula?
The optimal stocking quantities differ because there