Problema Solution
The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors.
C(x)=2400+50x
R(x)=810x-x^2
Determine the maximum profit of the company
Answer provided by our tutors
The profit of a company, in dollars, is the difference between the company's revenue and cost
P(x) = R(x) - C(x)
P(x) = 810x - x^2 - (2400 + 50x)
P(x) = - x^2 + 760x - 2400
To determine the maximum profit of the company, we need to find the maximum of the parabolic function:
P(x) = - x^2 + 760x - 2400
P max = c - b^2/(4a) where a= -1, b = 760, c = - 2400
P max = -2400 - (760)^2/(4(-1))
P max = $142,000 is the the maximum profit of the company.