Question

The owner of a video store has determined that the cost c, in dollars, of operating the store is approximately given by f(x) = 2x2- 22x + 660, where x is the number of videos rented daily. find the lowest cost to the nearest dollar.

Answer 1

2x^ 2-22x+660 =0
4x -22x +660 = 0
-18x = -660
-660/-18
x= 37
2(37)^2 -22(37)+660 = 5,322

Answer 2

Answer: $600

Explanation: The cost of the store is defined by the equation:

f(x) = 2x^2 - 22x + 660

Where x is the number of videos rented daily, if we want to find the minimum of a function, we need to see the point in wich the derivate is equal to zero, in this case we have:

f'(x) = 4*x - 22 = 0

x = 22/4 = 5.5

So if he rents 5.5, the total cost of the store is:

f(5.5) = 2*5.5^2 - 22*5.5 + 660 = 599.5 dollars

Rounding to the nearest dollar, we have a total minimal cost of 600 dollars