Question

an online furniture store sells chairs for $150 each and tables for $350 each. Every day, the store can ship a maximum of 24 pieces of furniture and must sell a minimum of $5400 worth of chairs and tables. Also, the store must sell at least 14 tables and a maximum of 6 chairs. If x 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

The problem can be solved graphically by plotting the system of inequalities representing the constraints on selling tables and chairs. The inequalities are based on the shipping limit, minimum sales value, and restrictions on the number of tables and chairs sold. One possible solution within the feasible region is selling 14 tables and 6 chairs.

Step-by-step explanation:

To solve this problem graphically, we need to set up a system of inequalities based on the given conditions. We have the following inequalities based on the prompt:

• The store can ship a maximum of 24 pieces of furniture: x + y ≤ 24
• The store must sell at least $5400 worth of furniture: 350x + 150y ≥ 5400
• At least 14 tables must be sold: x ≥ 14
• A maximum of 6 chairs can be sold: y ≤ 6

We represent tables with x and chairs with y. Plotting these inequalities on a coordinate plane will give us a feasible region. We then look for points within this region that satisfy all inequalities. One possible solution could be at the point where x = 14 (minimum tables) and y = 6 (maximum chairs), which fulfils all the conditions set by the inequalities. Therefore, selling 14 tables and 6 chairs is one possible combination that meets the store's requirements.