Giapetto's Woodcarving, Inc. manufactures two types of toys: soldiers and trains. Each soldier sold generate $3 in profit while each train generates $2 in profit. 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 labor and 1 hour of carpentry. Each week, Giapetto can obtain all the needed raw materials but only 100 finishing hours and 80 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Help Giapetto to maximize his profit.
a) Solve the linear program using the simplex method.
b) Solve the linear program using Solver or LINDO.