$1.$ Johnson Electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The production cost is $$5$ per each catalog. Data indicate that, on average, each printed catalog generates a profit of $$35$ from sales $($i$.$e$.,$ $$40$ revenue$).$ 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.

Cont. from the previous question

$2.$ The demand for the printed catalog is distributed as follows $($a selective part$)$:

Number of Catalogs $...60616263646566...$

Cumulative Probability $...0\mathrm{.}800\mathrm{.}830\mathrm{.}860\mathrm{.}890\mathrm{.}910\mathrm{.}930\mathrm{.}94...$

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.

$3.$ Consider the same supply chain setting as in Practice Problem $3$ in the Newsvendor lecture.

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?