1. a. The simulation indicates that 584 is the optimum stocking quantity. Daily profit at this stocking quantity is $331.4346. b. Using the newsvendor model, Cu = 1 - 0.2 = 0.8 and Co = .2. Cu /(Cu + Co) = .8. Using the spreadsheet, we found Q* = NORM.INV(.8,500,100) = 584.16. The simulation and newsvendor model give the same optimal stocking quantity.
2. a. According to the simulation spreadsheet, 4 hours of investment in creation maximizes daily profit at $371.33. b. Sheen would choose an effort level where the marginal benefit gained by the effort is equal to her marginal cost of expending the effort. To calculate the effort level, h, we equalize marginal cost and marginal benefit. Here (.8 * 50) / (2√h) = 10. Solving gives h = 4, or the same as the simulation. c. The optimal profit derived in this scenario is $371.33 per day, which is a $40 increase from the profit derived in problem #1, of $331.43.
3. a. Using the spreadsheet, Ralph’s optimal stocking quantity to maximize his profit is 516. b. The optimal stocking quantity differs from problem #2 because Ralph is incurring the cost of overstocking, which changes the critical ratio from .8 in problem #2 to .2. Because of the critical ratio change, Anna’s profit decreases as Ralph’s increases. This is consistent with the Newsvendor Model, which gives Cu=.2, Co=.8, for a critical ratio of .2. Using the formula in the spreadsheet, Q*=NORM.INV(.2,600,100)=515.837, gives the optimal stocking quantity of 516. c. Assuming that we only use whole numbers for her amount of time, Anna’s optimal effort is 2 hours with a profit of $261.93, a decrease from problem #2 of 4 hours. This is because Anna is now sharing her profit. d. If you decrease the transfer price, Anna’s effort level also decreases, and Ralph will increase his stocking quantity, adding to his profit. Anna’s effort level decreases because her profit decreases when Ralph buys the newspapers for less than $0.80. When the transfer price increases, the...
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