Q$1.$ Orbit Hyper Market $($OHM$)$ purchases knitted high quality winter clothes from both John Knitted Cloth Limited $($JKCL$),$ Overseas supplier and Babul All Weather Cloth Limited $($BAWC$),$ Indian Supplier. The clothes purchased from the Supplier is popular among the customers and is anticipated that the cloth demand will be normally distributed during the four$-$month season. Also, it is observed that the salvage value of the products purchased from both JKLC and BAWC are one fourth of their corresponding purchase price whereas OHM is generally lost the opportunity to earn a profit of half of the purchase price if the customer demand is not met during the season. The purchase price per unit of JKCL is higher than the purchase price of BAWC. The demand information for both the products in the season is anticipated as mentioned in Table.

a$)$ Determine the ratio of the order quantity of cloth "from JKCL to OHM" and "from BAWC to $\backslash (\backslash$mathrm$\{$OHM$\}^\{\backslash$prime $\backslash$prime$\}\backslash ).$ Assume that OHM places singe order in a season.

b$)$ Determine the optimum product availability if JKCL and BAWC will go for buyback contract with buy$-$back price of $0\mathrm{.}75$ of purchase price $($i$.$e$.$ price at which product is sold to OHM $)?$