Systems of Linear Equations from Word Problems

Task: Solve each problem and write a recommendation for the business owners. Provide a detailed explanation for your recommendation. Show your complete solution and graph.

A local government organized a week$-$long activity to support local and small businesses in the area. There are trade fairs, product promotions, and seminar workshops for new and upcoming businesses. As a business advisor, you are invited to give recommendations to help new and aspiring owners with their business dilemmas. Your recommendations will be judged based on the data accuracy, application of mathematical concepts, and graph accuracy.

The Good Nature Furniture is a sustainable furniture shop that aims to create high$-$quality tables and chairs made exclusively from reclaimed wood and other sustainably sourced wood.

Materials Needed Labor Required Net Profit per Unit

Table $60$ board feet $4$ hours P $500$

Chair $30$ board feet $5$ hours P $250$

Considerations: The shop has $4000$ board feet of lumber available and a staff who can provide $350$ hours of labor.

Concern: How many tables and chairs should they make to maximize the profit?