Problem $2.$ Consider a supplier and retailer under a wholesale price contract where the demand

is Normal$(1200,{340}^2),$ and $r=18\mathrm{.}99,v=0\mathrm{.}65,p_r=9,p_s=4,c_r=1\mathrm{.}2,c_s=3\mathrm{.}75,$ and $w=11.$

Calculate the order quantities that are optimal for the retailer and for the total supply chain, and

then verify that the supply chain is not coordinated.

Problem $3.$ Consider the supplier and retailer in Problem $2$ above, but now under a buyback

contract with $b=8.$ What value of the price $w$ will coordinate the supply chain? Report the

corresponding coordinated order quantities for the supplier and the retailer. Now instead suppose

that the supplier and retailer are under a revenue sharing contract with $=0\mathrm{.}6.$ What value of

the price $w$ will coordinate the supply chain?Consider the supplier and retailer in Problem $2$ above, but now under a buyback

contract with b $=8.$ What value of the price w will coordinate the supply chain? Report the

corresponding coordinated order quantities for the supplier and the retailer. Now instead suppose

that the supplier and retailer are under a revenue sharing contract with $\backslash$phi $=0\mathrm{.}6.$ What value of

the price w will coordinate the supply chain?

Problem $4.$ Problem $11\mathrm{.}1($part $($a$)$ only$)$ from Snyder and Shen, $2$nd edition, referenced in the

syllabus, available online through Clemson Libraries.

Problem $5.$ Consider a wholesale price contract with w $>$ cs$.$ Then prove that Q$$

r $$ Q$.$

Problem $6.$ Read Section $14\mathrm{.}8$ on quantity flexibility contracts from Snyder and Shen, $2$nd edition,

referenced in the syllabus, available online through Clemson Libraries. Then write a short note $($at

most one page$)$ on this topic.

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