91Ó°ÊÓ

A furniture company produces tables and chairs. Each table requires 1 hour in the assembly center and \(1 \frac{1}{3}\) hours in the finishing center. Each chair requires \(1 \frac{1}{2}\) hours in the assembly center and \(1 \frac{1}{2}\) hours in the finishing center. The assembly center is available 12 hours per day, and the finishing center is available 15 hours per day. Find and graph a system of inequalities describing all possible production levels.

A person plans to invest up to \(\$ 20,000\) in two different interest-bearing accounts. Each account is to contain at least \(\$ 5000 .\) Moreover, the amount in one account should be at least twice the amount in the other account. Find and graph a system of inequalities to describe the various amounts that can be deposited in each account.

For a concert event, there are \(\$ 30\) reserved seat tickets and \(\$ 20\) general admission tickets. There are 2000 reserved seats available, and fire regulations limit the number of paid ticket holders to 3000. The promoter must take in at least \(\$ 75,000\) in ticket sales. Find and graph a system of inequalities describing the different numbers of tickets that can be sold.

Describe two ways of solving for the constants in a partial fraction decomposition.

A person's maximum heart rate is \(220-x\) where \(x\) is the person's age in years for \(20 \leq x \leq 70\) The American Heart Association recommends that when a person exercises, the person should strive for a heart rate that is at least \(50 \%\) of the maximum and at most \(85 \%\) of the maximum. (a) Write a system of inequalities that describes the exercise target heart rate region. (b) Sketch a graph of the region in part (a). (c) Find two solutions to the system and interpret their meanings in the context of the problem.

Determine whether the statement is true or false. Justify your answer. If a system of three linear equations is inconsistent, then its graph has no points common to all three equations.