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)-2300+40x
R(x)=7800x-x^2
Determine the maximum profit of the company.
Determine the number of items that must be produced and sold to obtain the maximum profit.
Answer provided by our tutors
The profit of a company, in dollars, is the difference between the company's revenue and cost
R(x) - C(x) = 7800x-x^2 - (2300 + 40x) = - x^2 - 7760x - 2300
Determine the maximum profit of the company.
we need to find the maximum of the parabolic function
f(x) = - x^2 - 7760x - 2300
f max = c - b^2/(4a) where a= -1, b = -7760, c = 2300
f max = 2300 - (-7760)^2/(4(-1))
f max = $15,056,700 is the the maximum profit of the company
Determine the number of items that must be produced and sold to obtain the maximum profit
- x^2 - 7760x - 2300 = 15,056,700
by solving we find
x = - 3880
we got a negative number. No solution.
The equations for C(x)= 2300+40x, R(x)=7800x-x^2 might be wrong since x can not be negative.
Please check them up and resubmit the question.