Question

Ms. Tui is having new floors installed in her house. Floor Company A charges $90for installation and $9 per square yard of flooring. Floor Company B charges $50for installation and $13 for each square yard.

Answer 1

We have two cost functions.

Company A charges a fixed value of $90 and a variable cost of $9 per sq yd.

$C_A=90+9x$

Company B chargesa fixed value of $50 and a variable cost of $13 per sq yd.

$C_B=50+13x$

The breakeven point for the square yard of the floor, when both cost are the same, can be calculated as:

$\begin{gathered} C_A=C_B \\ 90+9x=50+13x \\ 90-50=13x-9x \\ 40=4x \\ x=\frac{40}{4} \\ x=10 \end{gathered}$

The breakeven point is x=10 sq yd.

If x>10, company B is more expensive that company A.