Linear Programming - Extra Credit You may work in groups of up to 4 on the following problem. Turn in one final formulation as well as the solution your group came up with. Include everyone's name. Problem (From Winston and Venkataramanan, Introduction To Mathematical Programming): Giapetto's woodcarving Giapetto's Woodcarving, Inc., manufactures two types of wooden toys: soldiers and trains. A soldier sells for $27 and uses $10 worth of raw materials. Each soldier that is manu- factured increases Giapetto's variable labor and overhead costs by $14. A train sells for $21 and uses $9 worth of raw materials. Each train built increases Giapetto's variable la- bor and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train requires 1 hour of finishing and 1 hour of car- pentry labor. Each week, Giapetto can obtain all the needed raw material but only 100 fin- ishing hours and 80 carpentry hours. Demand for trains is unlimited, but at most 40 sol- diers are bought each week. Giapetto wants to maximize weekly profit (revenues - costs). Formulate a mathematical model of Giapetto's situation that can be used to maximize Gi- apetto's weekly profit. Formulate and solve the linear program described above. Clearly define the decision variables. Decision variables: Objective Function: Constraints: Solution