$1.$ Johnson Electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The production cost is$$$$5$per catalog. Data indicate that, on average, each printed catalog generates $$40$ in revenue from sales $($i$.$e$.,$ $$35$ net profit$).$ What is the optimal service level for the catalog printing decision? Please identify Cu $($under$-$stocking cost$)$ and Co $($over$-$stocking cost$)$ to calculate the critical ratio, i$.$e$.,$ the optimal service level. Please briefly explain your calculation logic to show the work.

Please identify the optimal production quantity, i$.$e$.,$ the number of

catalogs to be printed, based on the optimal service level identified in the

previous question. Please explain your logic to show the work.

$3.$ The wholesaler buys newspapers from the publisher and distributes them to local newsstands. The wholesaler then sells the newspaper to the local newsvendors at$80$ cents$$per newspaper, and the local newsvendors sell the newspaper to the final customer at$1$ dollar$$each$.$ The wholesaler wants to induce the newsvendor to purchase more newspapers, so agrees to buy back unsold newspapers at a price of$$$$0\mathrm{.}50/$newspaper$.$ What is the optimal service level for the local newsvendor now? Please identify Cu $($under$-$stocking cost$)$ and Co $($over$-$stocking cost$)$ to calculate the critical ratio, i$.$e$.,$ the optimal service level. Please briefly explain your calculation logic to show the work. Hint: The buy$-$back price represents the salvage value of the unsold newspapers.

$4.$ What is the optimal service level for the local newsvendors if now the wholesaler agrees to buy back unsold newspapers at a price of$$$$0\mathrm{.}75/$newspaper$.?$ Please identify Cu $($under$-$stocking cost$)$ and Co $($over$-$stocking cost$)$ to calculate the critical ratio, i$.$e$.,$ the optimal service level. Please briefly explain your calculation logic to show the work.

$5.$ We have figured out in class that the optimal service level of the entire supply chain is$0\mathrm{.}80.$ This is the service level that maximizes the total profit of the chain.$$ Based on the service level, between the two candidate buy$-$back prices,$$$$0\mathrm{.}50/$newspaper and$$$$0\mathrm{.}75/$newspaper$,$which one would the wholesaler choose to induce a higher total profit?

$6.$ Compared to a buy$-$back contract, a revenue$-$sharing contract is generally better to incentivize local newsvendors to sell more newspapers.