Question

(Part B)Carrie is considering three different types if materials 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. (Part C)Based on the results from part B, which two statements correctly interpret actions the business should take?A.) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.B.) If material 1 is used, Carrie will earn a profit if she sells chairs for lower than $50 each.C.) If material 3 is used, Carrie will earn a profit if she sells chairs between $45 and $160 each.D.) If material 2 is used, Carrie will earn a profit if she sells chairs between $30 and $120 each.E.) If material 1 is used, Carrie will earn a profit of she sells chairs between $40 and $70 each.

Answer 1

The respective graphs are

For material 2:

and for material 3:

We can test each set of functions by substituying a value of x. For instance, when x= 100 we have

Material 1:

`\begin{gathered} R(100)=200000(100)-2000(100)^2 \\ R(100)=0 \end{gathered}`

and

`\begin{gathered} c(100)=5000000-20000(100) \\ c(100)=3000,000 \end{gathered}`

Material 2:

`\begin{gathered} R(100)=160000(100)-1000(100^2) \\ R(100)=6,000,000 \end{gathered}`

and

`\begin{gathered} C(100)=4000000-10000(100) \\ C(100)=3,000,000 \end{gathered}`

Material 3:

`\begin{gathered} R(100)=54000(100)-270(100^2) \\ R(100)=27,000,000 \end{gathered}`

and

`\begin{gathered} C(100)=2000000-5000(100) \\ C(100)=1,500,000 \end{gathered}`

By comparing results, we can see that material 3 can deliver the highest profit about 27,000,000-1,500,000= 25000000.