Essential Skills Chapter 8

1. Solving systems of linear equations Section 8.1

Example: Solve.

Answer: ,

2. Using matrices to solve systems of linear equations Section 8.2

Example: Solve using matrices.

Answer:

3. Solving systems of nonlinear equations Section 8.6

Example: Solve.

Answer: and

4. Graphing systems of linear inequalities Section 8.7

Example: Graph. Answer:

5. Problem solving with Linear Programming Section 8.8

Process	Hours, model A	Hours, model B
Assembling	2	2.5
Painting	4	1
Packaging	1	0.75

Example: A manufacturer produces two models of bicycles. The times (in hours) required for assembling, painting, and packaging each model are shown in the table.

The total times available for assembling, painting, and packaging are 4000 hours, 4800 hours, and 1500 hours, respectively. The profits per unit are $45 for model A and $50 for model B. How many of each type should be produced to maximize profit? What is the maximum profit?

Answer: 750 units of model A, 1000 units of model B; maximum profit: $83,750