# Using 584.162, the same as the Q*

Using the spreadsheet, we found that the optimal stocking quantity was 584. At that quantity daily profit is \$331.43.
With the given information we verified this number using the newsvendor model. Where Cu = 1 – 0.20 = 0.80 and Co = 0.2. Critical = 0.8 / (0.8 + 0.2) = 0.8. Which we used to calculate a Q* of 584.162, the same as the Q* in part a.

Using the spreadsheet, with an opportunity cost of \$10/hour, we found that she should invest 4 hours into the creation of the profile section. This would raise Q* to 685 and would maximize daily profits at \$371.33
This effort level was chosen because she needed an effort level that made the marginal cost of effort equal to the marginal benefit. When you set her marginal cost equal to the formula for her marginal benefit, and solve for h, you find that h=4.
The optimal profit found here is nearly \$40 greater than that in problem 1. This is likely because hours invested in the creation of the profile section is positively correlated with average daily demand. So when we increase the hours invested while adding no costs, we increase demand, thus increasing profits.

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Using the spreadsheet we found that, Ralph Armentrout’s optimal stocking quantity would be 516. Creating a profit of \$322, \$260.20 of which is Anna’s, with Ralph receiving \$62.14 in profit.
This optimal stocking quantity differs from the previous finding because now the Co = .8 and the Cu = .2, which gives a critical = .2 / (.2 + .8) = .2. Which, we then can calculate the Q* = 515.84.
Now the optimal h = 2 hours. This is due to the fact that Anna now is sharing a portion of the profits with Ralph.
As the transfer price decreases, so does the effort level for Anna, and there will be an increase in optimal stocking quantity for Ralph, which will increase his profit. The decrease in Anna’s effort level is due to the fact that when she lowers the transfer price below \$0.80, she decreases her profits. The opposite of this will occur if the transfer price is increased, Anna will increase effort, and Ralph will decrease stocking quantity.
Not sure

Using the simulation in the spreadsheet we found the optimal stocking quantity to be 409, the decrease from the optimal quantity of 516 in problem 3 is likely because even if the express is that when the express stocks out, Ralph will still profit from his own private paper.
In the previous problems there was no way to cover the losses of understocking however in problem 4 Ralph has his private paper that 40% of his customers will buy, providing a more profitable alternative if he is understocked. This creates different critical ratios, therefore creating different optimal quantity.
Ralph is now spending \$.03 on the cost of each newspaper making his Cu=1-.83-40%*0,4=.01 and a Co = 0.83. Giving a critical ratio of 0.012. Which we then derived a Q* of 274.29.

The lower buy-back price affects the cost of overstocking so that Ralph will lower his optimal stocking quantity. The optimal buy back price we found was \$0.75, which corresponds to a n optimal stocking quantity of 659, and a channel profit of \$369.80
We found the optimal transfer price to be \$0.99, corresponding to a buy back price of \$0.988, creating profits of \$372.62. This situation is very unlikely though, because Ralph will be profiting -\$24 and Anna will be making nearly \$1 on each sale. This profit is very similar to the profit we found in the second problem likely because the transfer price found is extremely close to the selling price of \$1. Due to this Anna has almost no risk when overstocking.
Ralph would lose his current incentive to keep a lower stock, and Anna would remain unchanged, as her marginal benefit would not change.  