Question

help please anyone good in calculus and please explain step by step it would be really great.

Answer 1

A consulting firm conducts training sessions for employees of various companies. The charge to a company sending employees to a session is $50 per employee, less $0.50 for each employee in excess of 10. That is, for example, if twelve employees are sent, the charge per employee would be $49.00 and the total prorated charge to the company would be 12(49.00)=$558.00. The consulting firm further has a fixed total charge for groups of x or more where x is the number that maximizes the prorated group charge. What should x be, and what is the maximum total group charge to the company?

Answer 2

@mathstudent55

Answer 3

first write equation for charge in terms of x:

\[C = x[50 - 0.5(x-10)] = x(55 - 0.5x)\]
\[C = 55x - 0.5x^{2}\]
we want to maximize charge so set derivative equal to zero
\[\frac{dC}{dx} = 55 - x = 0\]
\[x = 55\]
plug it into C equation to get max charge