Question

A kitchen table is being sold at a furniture store. These are the cost and revenue functions associated with the tables, where x
represents the selling price of a single table:
R(X) = -0.68x2 + 310x
C(x) = 43.6x + 36,176
Which two points represent breakeven for table sales?
(0, 36,176)
(140, 30,072)
(227, 35,330)
(260, 9,792)
(380, 19,608)

Answer 1

Answer:

(140, 30,072) and (380, 19608).

Step-by-step explanation:

We are given that the revenue function for selling the kitchen table given its price is:

$R(x)=-0.68x^2+310x$

And the cost function is:

$C(x)=-43.6x+36176$

At the breakeven point, the revenue equals the cost. Therefore:

$R(x)=C(x)$

Substitute:

$-0.68x^2+310x=-43.6x+36176$

We can solve for x.

Adding 0.68x² to both sides and subtracting 310x from both sides yields:

$0.68x^2-353.6x+36176=0$

We can use the quadratic formula:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 0.68, b = -353.6, and c = 36176. Substitute:

$\displaystyle x=\frac{-(-353.6)\pm\sqrt{(-353.6)^2-4(0.68)(36176)}}{2(0.68)}$

Simplify:

$\displaystyle x=\frac{353.6\pm\sqrt{26684.24}}{1.36}$

So, our two solutions are:

$\displaystyle x=\frac{353.6+\sqrt{26684.24}}{1.36}\text{ or } x=\frac{353.6-\sqrt{26684.24}}{1.36}$

Use a calculator:

$x\approx 380\text{ or } x\approx 140$

Our answers are:

(140, 30,072) and (380, 19608).