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 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 hour 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 80 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Giapetto wants to maximize weekly profit (revenues-costs). A) Calculate the range of variation for the utilities of soldiers and trains. B) How much would you be willing to pay for one more hour of finishing? Why? C) If there were 10 more hours of finishing, what would be the new optimal solution?
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 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 hour 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 80 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Giapetto wants to maximize weekly profit (revenues-costs).
A) Calculate the range of variation for the utilities of soldiers and trains.
B) How much would you be willing to pay for one more hour of finishing? Why?
C) If there were 10 more hours of finishing, what would be the new optimal solution?
D) The factory wants to know if it is in their interest to make wooden boats. The sale price of each boat would be $ 25, using $ 10 of raw material and general costs of $ 10. To manufacture it requires 1 hour of finishing and 1 hour of carpentry. Would it be convenient to produce it? Justify your answer.
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