Question

Alyssa Poindexter Context Inequality Systems Graphically An online furniture store sells chairs for $200 each and tables for $450 each. Every day, the store can ship a maximum of 20 pieces of furniture and must sell at least $4800 worth of chairs and tables. If z represents the number of tables sold and Y represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

First of all, it is necessary to determine the system of inequelities. Use the given information:

If z represents the number of tables sold, then, 200z represents the money of the sold of z tables. If y represents the number of chairs sold, then, 450y represents the money of the sold of y chairs.

Every day, the store can ship a maximum of 20 pieces of furniture. This can be written as follow:

y + z ≤ 20

Every day, the store must sell at least $4800 worth of chairs and tables. This can be written as follow:

450y + 200z ≥ 4800

Solve the previous inequalities for z:

y + z ≤ 20

z ≤ -y + 20

450y + 200z ≥ 4800

200z ≥ -450y + 4800

z ≥ -2.25y + 24

The graph of the previous inequalities are:

The red shaded region is the solution for the first inequality, and the green shaded region is the solution for the second one.

The region at which both solution intersect each other is the solution to the system.

One possible solution is for exmaple, y = 10 and z = 5, beacue this point is in the region which is solution to the system.