Question

K

If the cost, C(x), for manufacturing x units of a certain product is given by
C(x)=x²-19x+40
find the number of units manufactured at a cost of $9850.
The number of units is.

Answer 1

Explanation:

C(x) = x² - 19x + 40 (cost equation)

9850 = x² - 19x + 40 (substitute 9850 for C(x))

Rearranging the equation, we get:

x² - 19x + 9810 = 0

We can use the quadratic formula to solve for x:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = -19, and c = 9810

x = (-(-19) ± sqrt((-19)² - 4(1)(9810))) / 2(1)

x = (19 ± sqrt(19² - 4(1)(9810))) / 2

x = (19 ± sqrt(361 - 39240)) / 2

x = (19 ± sqrt(-38879)) / 2

Since the value under the square root is negative, there are no real solutions for x. This means that it's not possible to manufacture a number of units at a cost of $9850 using this cost equation.