In the supply network lecture, we discussed identifying the optimal material flow in a supply chain to match supply and demand. More specifically, we discussed two examples: $1)$ BuyPC.com case and $2)$ a simple supply chains with $2$ plants, $2$ distribution centers $($DCs$)$ and $3$ customers. If you were hired by a company and were tasked to solve the BuyPC.com case using optimization tools, how would you do it$?$ To answer this question, let$$s consider the LP formulation for the simpler $2$Plant$/2$ DC supply chain problem setting: what if the company says we have $15$ possible DCs and we would like to utilize the best $2$ only to satisfy the demand! Now as a systems engineer or engineering manager, you are asked to formulate an optimization model to solve this automatically $($meaning select the best $2$ DCs out of $15$ DCs through optimization$).$ How would you modify the LP model: in other words a$)$ what additional decision would you define? b$)$ How would you modify the objective function and c$)$ How would you modify the constraints?In the supply network lecture, we discussed identifying the optimal material flow in a supply chain to match supply and demand. More specifically, we discussed two examples: $1)$ BuyPC.com case and $2)$ a simple supply chains with $2$ plants, $2$ distribution centers $($DCs$)$ and $3$ customers. If you were hired by a company and were tasked to solve the BuyPC.com case using optimization tools, how would you do it$?$ To answer this question, let$$s consider the LP formulation for the simpler $2$Plant$/2$ DC supply chain problem setting: what if the company says we have $15$ possible DCs and we would like to utilize the best $2$ only to satisfy the demand! Now as a systems engineer or engineering manager, you are asked to formulate an optimization model to solve this automatically $($meaning select the best $2$ DCs out of $15$ DCs through optimization$).$ How would you modify the LP model: in other words a$)$ what additional decision would you define? b$)$ How would you modify the objective function and c$)$ How would you modify the constraints?