Please help me asap

Question

You are opening a widget selling business and want to know what you should sell each widget for. Your research team has found that if you make the price “x”, your total sales will be S(x)=-200x²+70,000x. Also, when the price is ‘x’, the total cost will be C(x)= -22,000x+8,375,000.  Find the price which makes the total sales and total cost equal. Then find the corresponding cost.

Answer 1

If you are trying to make the total sales and total cost equal to each other then you make S(x) = C(x) or:

-200x² + 70000x = -22000x + 8375000

This is a quadratic equation and the way we typically solve quadratics is to set them equal to zero. So, let's move the terms on the right over to the left by adding 22000x and subtracting 8375000 from both sides:

-200x² + 92000x - 8375000 = 0 [now divide both sides by -200

x² - 460x + 41875 = 0 [now factor it or use the quadratic formula. I'll factor:

(x - 125)(x - 335) = 0

Then set each piece equal to zero to find x:

x - 125 = 0 or x = 125

x - 335 = 0 or x = 335

These 2 prices ($125 and $335) will make the sales and cost equal. The value of the cost for each is:

C(125) = $5,625,000

C(335) = $1,005,000