Question

The revenue associated with selling vitamins is R(x) = 500x - 0.001x^2 where R is the revenue in dollars and x is the number of bottles of vitamins sold. Determine how many bottles of vitamins should be sold to maximize the revenue.

A. 250,000
B. 500,000
C. 1,000,000
D. 1,500,000

Answer 1

To maximize revenue from selling vitamins, the turning point of the function R(x) = 500x - 0.001x^2 is calculated using the vertex formula -b/(2a), resulting in the sale of 250,000 bottles.

Step-by-step explanation:

To determine how many bottles of vitamins should be sold to maximize revenue, one must find the vertex of the parabolic revenue function given by R(x) = 500x - 0.001x^2. The vertex can be found by using the formula -b/(2a) where a and b are the coefficients of x^2 and x in the quadratic function respectively. For the function R(x), a is -0.001 and b is 500.

Plugging into the vertex formula gives us x = -500 / (2 * -0.001) = 250,000. Therefore, to maximize revenue, 250,000 bottles of vitamins must be sold, which corresponds to answer choice A.