Linear Programming Problem 1:

George's Woodcarving Company manufactures two types of woodentoys: soldiers and trains. A soldier sells for $27 and uses $10worth of raw materials. Each soldier manufactured increasesGeorge's variable labor and overhead costs by $14. A train sellsfor $21 and uses $9 worth of raw materials. Each Train builtincreases George's variable labor and overhead costs by $10. Themanufacture of wooden soldiers and trains requires two types ofskilled labor: carpentry and finishing. A soldier requires 3 hoursof carpentry labor and 2 hours of finishing labor. A train requires4 hours of carpentry labor and 1 hour of finishing labor. Eachweek, George's can obtain all the needed raw material but only 240carpentry hours and 100 finishing hours. Demand for trains isunlimited, but at most 28 soldiers are bought each week. Georgewishes to maximize weekly profit (revenue – costs). The companywants to find out the optimal production strategy that maximizesthe weekly profit.

First solve this problem graphically or using the Solver. Havethe solved graph or spreadsheet ready. For graphical approach, youneed to solve for the optimal solution by solving simultaneousequations 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 manycarpentry hours are required?

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

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

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

8. What is the maximum total profit?

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

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