Consider the classical buyer$-$vendor problem where the vendor orders in bulks and dispatches

to the buyer in smaller quantities. That is$,$ the vendor's replenishment order quantity $Q_w$ is an integer $(n)$

multiple of the buyer's order quantity $(Q_t).$ Assume that the following relation holds.

$0\frac{K_w{h}_r}{K_r{h}_w}2$

a$)$ Find expressions for the buyer's order quantity resulting from the optimal centralized and

decentralized solutions.

b$)$ Compute the ratio $Q\frac{c^{**}}{Q}{d}^{**}$ and comment on the implications of the ratio found.

c$)$ Consider the total supply chain costs resulting from the two solutions. Derive a closed form

expression for the:

Total supply chain cost under centralized solution$/$ Total supply chain cost under decentralized solution