Suppose now the manufacturer and the retailer still work separately from each other. Design a franchise contract so that $(1)$ together they can achieve the total profit as in the integration case $($Part II$)$ and $(2)$ it will make the manufacturer$$s profit triple the retailer$$s profit, i$.$e$.,\backslash$pi M$=3\backslash$pi R$.$

$($Q$2$E$).$ How to design this franchise contract?