Question

Carrie is considering three different types of material for her chairs. Depending on the price she sets for each chair, the costs and revenues for each type of material will generate different costs and revenues for her business. In the functions in the table, x is the price of each chair. The functions give the revenue (R) and costs (C) that Carrie's business can expect in a year at a given price for the item. Use graphing tools to examine the graphs for each set of equations. Then select the correct answer from each drop-down menu

Answer 1

For Material 1, we have the following graph:

Where the parabola represents Revenue and the straight line represents Costs.

For Material 2, we have:

For Material 3, we have:

As you can observe, material 2 gives the highest revenue. For a price of 80, the revenue is 6.4 million. Now, we use the linear equation to find the cost.

`y=4,000,000-10,000\cdot80=4,000,000-800,000=3,200,000`

Then, we subtract the revenue and the cost to find the profit.

`6,400,000-3,200,000=3,200,000`

Hence, profit is 3,200,000.

First statement: Material 2 can deliver the highest profit of about 3,200,000.

Second statement: Material 3 earns profit for the widest range of prices from 0 to 200.