Question

A company estimates that its cost and revenue can be modeled by the functions

C(x) = -0.75x + 100x+20,000 and R(x) =150x+100 where a is the number of units
produced. The company's profit. P. is modeled by R(x)-C(x). Find the profit equation and determine the profit when 1.000,000 units are produced.

Answer 1

The company's profit equation is P(x) = 50x - 19,900. When 1,000,000 units are produced, the profit is $49,980,100.

Step-by-step explanation:

The company's profit equation P(x) can be determined by subtracting the cost function C(x) from the revenue function R(x). First, let's correct the cost function as it seems to have a typo:

C(x) = 100x + 20,000.

Now, calculate profit P(x) by finding R(x) - C(x):

P(x) = R(x) - C(x) = (150x + 100) - (100x + 20,000).

After simplifying:

P(x) = 50x - 19,900.

Now, to determine the profit when 1,000,000 units are produced, plug in x = 1,000,000:

P(1,000,000) = 50(1,000,000) - 19,900 = 50,000,000 - 19,900 = 49,980,100.

Therefore, the profit when 1,000,000 units are produced is $49,980,100.