We now consider using a revenue sharing contract. We start with a wholesale price w of $$0\mathrm{.}75$ and a revenue share percentage y of $0\mathrm{.}7.$ a$.$ What is the retailer$$s optimal order quantity? What can you say on this value? b$.$ Compute the retailer$$s expected profit and the supplier$$s expected profit under the above revenue sharing contract. What can you conclude? c$.$ When comparing the wholesale price contract to the revenue sharing contract, who benefits? Justify your answer. $4.$ In Part $3$b$,$ you calculated the expected profit earned by the supplier and by the retailer. In some settings, to incentivize the retailer to sign on$,$ the supplier needs to guarantee a minimum expected profit level to the retailer. Find the wholesale price w and the revenue share percentage y that maximize the supplier$$s expected profit while ensuring the retailer makes at least as much as under the wholesale price contract $($see Part $1$b$).$