Question

Linear Programming Problem 1:

George's Woodcarving Company manufactures two types of wooden toys: soldiers and trains. A soldier sells for $27 and uses $10 worth of raw materials. Each soldier manufactured increases George's variable labor and overhead costs by $14. A train sells for $21 and uses $9 worth of raw materials. Each Train built increases George'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 3 hours of carpentry labor and 2 hours of finishing labor. A train requires 4 hours of carpentry labor and 1 hour of finishing labor. Each week, George's can obtain all the needed raw material but only 240 carpentry hours and 100 finishing hours. Demand for trains is unlimited, but at most 28 soldiers are bought each week. George wishes to maximize weekly profit (revenue – costs). The company wants to find out the optimal production strategy that maximizes the weekly profit.

First solve this problem graphically or using the Solver. Have the solved graph or spreadsheet ready. For graphical approach, you need to solve for the optimal solution by solving simultaneous equations after graphing.

Then answer the quiz questions.

1. How many decision variables are in this problem?

2. How many finishing hours are available in this problem?

3. What is the unit profit of a toy soldier? $____.

4. To produce 5 toy soldiers and 5 toy trains, how many carpentry hours are required?

5. To produce 5 toy soldiers and 10 toy trains, how many finishing hours are required?

6. In the optimal solution, how many toy soldiers are produced?

7. In the optimal solution, how many toy trains are produced?

8. What is the maximum total profit?

9. In the optimal solution, how many hours of carpentry labor in total are used?

10. In the optimal solution, how many hours of finishing labor in total are unused?

Answer 1