Manufactures two types of wooden toys

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Reference no: EM132300394

Giapetto’s Woodcarving, Inc., manufactures two types of wooden toys: soldiers and trains. A soldier sells for $27 and uses $9.5 worth of raw materials. Each soldier that is manufactured 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 labor 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 hours of finishing labor and 1 hour of carpentry labor. Each week, Giapetto can obtain all the needed raw material but only 100 finishing hours and 90 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Giapetto wishes to maximize weekly profit (revenues – costs). A formulation of a mathematical model of Giapetto’s situation that can be used to maximize Giapetto’s weekly profit is given below.

Formulation Let x1 be the number of soldiers to be made Let x2 be the number of trains to be made The formulation is max z ? 3.5x1 ? 2x2 s.t. 2x1 ? x2 ?100 x1 ? x2 ? 90 x1 ? 50 x1,x2 ?0 (profit) (finishing labor) (carpentry labor) (soldier demand is limited)

a) Use excel/LINGO to help solve these problems and print out the sensitivity reports or copy images into your solution (no need to upload files), use the report to answer the following questions.

b) How many carpentry hours need to be available for the current optimal solution to remain feasible?

c) If trains contribute $2.50 to profit instead of $2, how many trains and soldiers should be made, and what is the profit?

d) Mathematically calculate the optimality range for the profit of both trains and soldiers. Confirm your results with the solver report. Show all your work.

e) How much would Giapetto be willing to pay for 10 additional finishing hours? Can you answer the same question for 45 finishing hours?

Reference no: EM132300394

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