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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 Functions Associated With The Tables Where X Represents The Selling Price Of A class=

Sagot :

xKelvin

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:

[tex]R(x)=-0.68x^2+310x[/tex]

And the cost function is:

[tex]C(x)=-43.6x+36176[/tex]

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

[tex]R(x)=C(x)[/tex]

Substitute:

[tex]-0.68x^2+310x=-43.6x+36176[/tex]

We can solve for x.

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

[tex]0.68x^2-353.6x+36176=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

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

[tex]\displaystyle x=\frac{-(-353.6)\pm\sqrt{(-353.6)^2-4(0.68)(36176)}}{2(0.68)}[/tex]

Simplify:

[tex]\displaystyle x=\frac{353.6\pm\sqrt{26684.24}}{1.36}[/tex]

So, our two solutions are:

[tex]\displaystyle x=\frac{353.6+\sqrt{26684.24}}{1.36}\text{ or } x=\frac{353.6-\sqrt{26684.24}}{1.36}[/tex]

Use a calculator:

[tex]x\approx 380\text{ or } x\approx 140[/tex]

Our answers are:

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

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