Question

If the cost, C(x), for manufacturing x units of a certain product is given by C(x)=x²-18x+31 find the number of units manufactured at a cost of $9950.

Answer 1

Explanation:

So, you have the equation:

x² - 18x + 31 = 9950

First, rearrange the equation to put it in the standard quadratic form:

x² - 18x + 31 - 9950 = 0

x² - 18x - 9919 = 0

Now, you can use the quadratic formula to solve for x:

The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a

For the equation x² - 18x - 9919 = 0, the coefficients are:

a = 1

b = -18

c = -9919

Putting these values into the quadratic formula:

x = (18 ± √((-18)² - 4 * 1 * (-9919))) / (2 * 1)

x = (18 ± √(324 + 39676)) / 2

x = (18 ± √40000) / 2

x = (18 ± 200) / 2

Now, you have two possible solutions:

x = (18 + 200) / 2 = 218 / 2 = 109

x = (18 - 200) / 2 = -182 / 2 = -91

Since you can't have a negative number of units in this context, the valid solution is x = 109.

Therefore, the number of units manufactured at a cost of $9950 is 109 units.