Chapter 6.6, Problem 17E

Write a system of equations, and use the inverse of the coefficient matrix to solve each system of equations. (See Example 1.)

Furniture Manufacturing A Colorado-based company makes artisanal dining room furniture. A buffet requires 15 hours for cutting, 20hours for assembly, and 5 hours for finishing. A chair requires 5 hoursfor cutting, 8 hours for assembly, and 5 hours for finishing. A table requires 10 hours for cutting, 6 hours for assembly, and 6 hours forfinishing. The cutting department has 4900 hours of labor availableeach week, the assembly department has 6600 hours available, and the finishing department has 3900 hours available. How many pieces ofeach type of furniture should be produced each week if the factory is to run at full capacity?