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?
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Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- Floral Design: A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $300 allocated for the centerpieces and wants each centerpiece to contain 12 flowers, with twice as many roses as the number of irises and lilies combined. (a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system. (b) Solve your system of linear equations using an inverse matrix. Find the number of flowers of each type that the florist can use to create the 10 centerpieces.arrow_forwardWrite the system of equations that that corresponds to the augmented matrix. 203. [220021301| 12 2]arrow_forwardFor a system of two linear equations in two variables, aHow many solutions are possible? bWhat is meant by an inconsistent system? cWhat is meant by a dependent system?arrow_forward
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