A product can be produced at a total cost dollars, where x is the number produced. If the total revenue is given by dollars, find the maximum profit. Round your answer to the nearest dollar.
A)

Question

A product can be produced at a total cost  dollars, where x is the number produced. If the total revenue is given by  dollars, find the maximum profit. Round your answer to the nearest dollar. ​​
A) ​

Quizplus · Accepted Answer

The profit function is given by: P(x) = R(x) - C(x)
Where P(x) is the profit at x units, R(x) is the revenue at x units, and C(x) is the cost at x units.

Substituting the given expressions for R(x) and C(x), we have:
P(x) = (20x - 0.02x^2) - (11x)
P(x) = -0.02x^2 + 9x

To find the maximum profit, we need to find the vertex of the parabola representing the profit function. The x-coordinate of the vertex is given by:
x = -b/2a
x = -9/(-0.04)
x = 225

Therefore, the maximum profit is achieved when 225 units are produced.
P(225) = -0.02(225)^2 + 9(225)
P(225) = $1012.50, which rounds to $1013.

Therefore, the best choice is B, with a maximum profit of $1013.

A Product Can Be Produced at a Total Cost