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

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

Explanation:

i got it right

Answer 2

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

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=(-b\pm√(b^2-4ac))/(2a)`

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

`\displaystyle x=(-(-353.6)\pm√((-353.6)^2-4(0.68)(36176)))/(2(0.68))`

Simplify:

`\displaystyle x=(353.6\pm√(26684.24))/(1.36)`

So, our two solutions are:

`\displaystyle x=(353.6+√(26684.24))/(1.36)\text{ or } x=(353.6-√(26684.24))/(1.36)`

Use a calculator:

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

Our answers are:

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