Question

Suppose that the price per unit in dollars of a cell phone production is modeled by p=55−0.0125x, where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R=x⋅p. Find the production level that will maximize revenue.

Answer 1

Answer: At x = 2200 level of production, it will get maximum revenue.

Step-by-step explanation:

Since we have given that

p = 55-0.0125x

and Revenue function is given by

$R=x.p\\\\R=x(55-0.0.125x)\\\\R(x)=55x-0.0125x^2$

We will take the first derivative of it.

$R'(x)=55-0.025x$

Now,we will find the critical points :

$55-0.025x=0\\\\0.025x=55\\\\x=\dfrac{55}{0.025}\\\\x=2200$

and R''(x)=-0.025<0, so it will get maximum revenue.

Hence, At x = 2200 level of production, it will get maximum revenue.