229k views
5 votes
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)

A kitchen table is being sold at a furniture store. These are the cost and revenue-example-1
User Xknozi
by
5.1k points

2 Answers

4 votes

Answer:

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

Explanation:

i got it right

User Brenzo
by
5.2k points
3 votes

Answer:

(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 0.68 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).

User BennyP
by
4.8k points