$3.$ Consider the same supply chain setting as in Practice Problem $3$ in the Newsvendor lecture. The wholesaler buys newspapers from the publisher and distribute 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, and thus agree to buy back unsold newspapers at a price of $$0\mathrm{.}50/$newspaper$.$ What is the optimal service level for the local newsvendor now?

$4.$ What is the optimal service level for the local newsvendor now if the wholesaler agrees to buy back unsold newspapers at a price of $$0\mathrm{.}75/$newspaper$.?$

$5.$ 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, $$0\mathrm{.}60/$newspaper and $$0\mathrm{.}75/$newspaper$,$ which one would the wholesaler choose to induce a higher total

$6.$ Compared to a buy$-$back contract, a revenue$-$sharing contract is generally better to incentivize local newsvendors to sell more newspapers. $(10$ points$)$

Is the statement True or False?profit?