Question

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 4,000 finishing hours and 2,200 carpentry hours. Demand for trains is at least 200 each month and must be met, but at most 250 soldiers 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.

Answer 1

To maximize ABC's monthly profit, we need to formulate an LP model with decision variables, objective function, and constraints. The objective is to maximize profit, considering the costs and revenues associated with producing soldiers and trains. By solving this linear programming model, ABC can determine the optimal production quantities.

Step-by-step explanation:

To formulate an LP model that can be used to maximize ABC's monthly profit, we need to define decision variables, objective function, and constraints. Let's assume that x represents the number of soldiers produced, and y represents the number of trains produced. The objective function would be to maximize profit, which can be expressed as:

Maximize Profit = (29x + 22y) - (10x + 7y + 12x + 10y)

We also need to consider the following constraints:

1. Raw material constraint: 10x + 7y <= available raw materials
2. Finishing labor constraint: 4x + 2y <= available finishing hours
3. Carpentry labor constraint: 3x + y <= available carpentry hours
4. Demand constraint: x <= 250 and y >= 200

These constraints restrict the production of soldiers and trains based on the available resources and demand. By solving this linear programming model, ABC Woodcarving can determine the optimal production quantities to maximize their monthly profit.