$1(25$ points$)$ The ABC lumber company has three sources of wood and five markets where wood is demanded. The annual quantity of wood available in the supply sources $1,2,$ and $3$ are $15,20,$ and $15$ million board feet, respectively. The amount that can be sold at markets $1,2,3,4,$ and $5$ is $11,12,9,10,$ and $8$ million board feet, respectively. The company currently transports all of the wood by train. It wishes to evaluate its transportation schedule, possibly shifting some or all of its transportation to ships. The unit cost of shipment $($in $$10,000$ along the various routes using both methods is described in the table below.The management needs to decide to what extent to continue to rely on rail transportation.$$a$)$ Formulate a linear programming model for the ABC lumber company for the case that this company uses only rail transport and write out the mathematical notation of the entire model.$$Using table a$,$ we can create this mathematical model.$$Min $51$s$1$m$1+62$s$1$m$2+35$s$1$m$3+45$s$1$m$4+56$s$1$m$5+59$s$2$m$1+68$s$2$m$2+50$s$2$m$3+39$s$2$m$4+46$s$2$m$5+49$s$3$m$1+56$s$3$m$2+53$s$3$m$3+51$s$3$m$4+37$w$3$m$5$S$.$T$.$:$$s$1$m$1+$ s$2$m$1+$ s$3$m$1>=11$s$1$m$2+$ s$2$m$2+$ s$3$m$2>=12$S$1$m$3+$ s$2$m$3+$s$3$m$3$b$)$ Solve the problem in $($a$)$ using Excel. Be sure to upload the spreadsheet. See excel sheet.$$c$)$ Write down and interpret the optimal values for the objective function, shadow prices, decision variables, and reduced costs.$$Optimal Values $-$Shadow Prices $-$Decision Variables $-$Reduced Costs $-$d$)$ Formulate a linear programming model for the ABC lumber company for the case that this company uses only ship transport and write out the mathematical notation of the entire model.$$PLEASE DO C AND D$!!$