1. (LP PROBLEM) Write LP model for the problem given below, draw the graph which includes all lines, show the feasible solution area, find the profits of all corners, and find optimal solution. Please use Corner Method to solve the problem. (25 points) 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. Note that Profit=Revenue- All costs (raw material + labor and overhead)