ABC Woodcarving manufactures two types of wooden toys: soldiers and trains. A soldier sells for $29 and uses $10 worth of raw materials. Each soldier that is manufactured increases ABC’s variable labor and overhead costs by $12. A train sells for $22 and uses $7 worth of raw materials. Each train built increases ABC’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 4 hours of finishing labor and 3 hour of carpentry labor. A train requires 2 hour of finishing and 1 hour of carpentry labor. Each month, ABC can obtain all the needed raw material but only 4,200 finishing hours and 2,000 carpentry hours. Demand for trains is unlimited, but at most 220 trains are bought each month. ABC wants to maximize monthly profit (revenues – costs). Formulate an LP model that can be used to maximize ABC’s monthly profit. (a) Step 1: Define the decision variables precisely and completely (e.g., let X1 = … and X2 = …, etc.). __________________________________________________________________________________________ __________________________________________________________________________________________ (b) Step 2: State the objective function. ___________________________________________________________________________________________ (c) Step 3: Specify the constraints.
ABC Woodcarving manufactures two types of wooden toys: soldiers and trains. A soldier sells for $29 and uses
$10 worth of raw materials. Each soldier that is manufactured increases ABC’s variable labor and overhead costs
by $12. A train sells for $22 and uses $7 worth of raw materials. Each train built increases ABC’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 4 hours of finishing labor and 3 hour of carpentry labor. A train requires
2 hour of finishing and 1 hour of carpentry labor. Each month, ABC can obtain all the needed raw material but only
4,200 finishing hours and 2,000 carpentry hours. Demand for trains is unlimited, but at most 220 trains are bought
each month. ABC wants to maximize monthly profit (revenues – costs). Formulate an LP model that can be used to
maximize ABC’s monthly profit.
(a) Step 1: Define the decision variables precisely and completely (e.g., let X1 = … and X2 = …, etc.).
__________________________________________________________________________________________
__________________________________________________________________________________________
(b) Step 2: State the objective function.
___________________________________________________________________________________________
(c) Step 3: Specify the constraints.
___________________________________________ ___________________________________________
___________________________________________ ___________________________________________
___________________________________________ ___________________________________________
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