A manufacturer estimates that its product can be produced at a total cost of C(x) = 45,000 + 100x + x3 dollars. If the manufacturer's total revenue from the sale of x units is R(x) = 4000x dollars, determine the level of production x that will maximize the profit. (Round your answer to the nearest whole number.)

x = 1950 units

Step-by-step explanation:

We need to maximize Profit (P(x)). We know:

Profit = Revenue -  Cost

So,

This follows quadratic equation of the form  

So, matching, we have:

a = -1

b = 3900

c = -45,000

The max occurs at the value  

So, the level of production, x , that will maximize profit is:

75

step-by-step explanation: