Question

At a computer repair shop, the total revenue, r(x), of refurbishing x computers can be represented by the function r(x) = -3x² + 36x. How many computers must be refurbished to maximize the shop's revenue?

1) 108
2) 12
3) 6
4) 3

Answer 1

The maximum revenue for refurbishing computers is achieved when the shop refurbishes 6 computers, which is determined by finding the vertex of the quadratic function representing revenue.

Step-by-step explanation:

To find out how many computers must be refurbished to maximize the shop's revenue, using the function r(x) = -3x² + 36x, we need to identify the vertex of the parabola represented by the quadratic equation. This vertex will give us the maximum point since the coefficient of the x² term is negative, which indicates a downward-facing parabola.

We use the formula -b/(2a) to find the x-value of the vertex, where a and b are the coefficients of the x² and x terms, respectively. In the function r(x) = -3x² + 36x, a = -3 and b = 36. Therefore, the x-value of the vertex is:

x = -b/(2a) = -36/(2*(-3)) = 6

The shop must refurbish 6 computers to maximize its revenue. Option 3) is the correct answer.