Respuesta :
The maximum profit that the considered company can get is 142,400 bucks. That profit is earned when input x (the number of items produced) is 380
How to obtain the maximum value of a function?
To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
The missing part of question is:
" [tex]C(x)=2000+70x[/tex], [tex]R(x)=830x-x^2[/tex]
A. Determine the maximum profit of the company.
B. Determine the number of items that must be produced and sold to obtain the maximum profit"
The profit is the difference between the revenue and the cost, so we get:
[tex]P(x) = R(x) - C(x) = 760x - x^2 - 2000[/tex]
Finding its first and second rate with respect to x:
[tex]P'(x) = 760 -2x\\P''(x) = -2[/tex]
Equating first rate to 0 to get the critical values:
[tex]P'(x) = 0 \implies 760 = 2x \implies x = 380[/tex]
The second rate is < 0 for any x, x = 380 is minima, and x = 380 being only critical value, it is global maximum.
At x = 380, the profit evaluates to:
[tex]P(x) = 760x - x^2 - 2000\\P(380) = 760(380) - (380)^2 - 2000 = (380)^2 - 2000\\P(380) = 142400[/tex]
Thus, the maximum profit that the considered company can get is 142,400 bucks. That profit is earned when input x (the number of items produced) is 380
Learn more about maxima and minima of a function here:
https://brainly.com/question/13333267
