1) a. Sheen should stock the optimal stocking quantity in this situation, which is 584 newspapers. The expected profit at this stocking quantity is $331.44. b. Q= µ+Φ-1(Cu/(Cu+C0))δ Q=500+ Φ-1(.8/(.2+.8))100 Q=500+(..7881)(100) Q=579 This is off by 5 newspapers from the model given in the spreadsheet, which results in a $.03 difference in profits. 2) a. With the opportunity cost of her time per hour being equal to $10, Sheen should invest 4 hours daily into the creation of the profile section. This would raise here optimal stocking quantity to 685 newspapers and would increase her expected daily profit to $371.33. b. Sheen’s choice of effort level, h, to be 4 hours was chosen because, in order to maximize profit, she would need an effort level that made the marginal cost of her effort equal to the marginal benefit. The marginal cost(opportunity cost) of her effort was is $10/hr. The marginal benefit equated to (0.8 *50)/(2*√h). When set equal to each other, the optimal # of hours invested comes out to be 4. c. The optimal profit under this model is greater because an increase the hours invested in creating the profile section, h, is in direct relation to an increase in average daily demand. With an increase in demand/sales, and no increase in fixed or variable costs, profit will increase.
3) a. Armentrout’s optimal stocking quantity is equal to 516 newspapers. This creates of channel profit of $322 and makes Anna’s profit equal to $260.20. This stocking quantity maximizes Armentrout’s profit in this situation at $62.14. b. The optimal stocking quantity differs from that of Problem 2 because with the addition of Ralph to the channel, there is now an extra step in the supply chain and Ralph’s revenue to cost ratio differs from Anna’s in Problem 2. Because of this, it is to Ralph’s benefit to stock less newspapers in order to maximize his own profits. Anna has no control over the stocking quantity and will likely never maximize her profits. c. The new optimal...
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