Profits and functions

[Janay123]

Annual profit in thousands of dollars is given by the function, P(x) = 200√ x - 3 + 10,000, where x is the number of items sold in thousands, x ≥ 3.

1.describe the meaning of the number 3 in the formula, in terms of its meaning in relation to the profit.
2.describe the meaning of the number 10,000 in the formula, in terms of its meaning in relation to the profit.
3.find the profit for 5 different values of x
4.will this profit function have a maximum, if so, what is it?
5.what steps should the company take to prepare for your answer to part 5?

 

[tkhunny]

This appears to be a talking problem. You had better start talking.

 

[rbcc]

Hi,

1. the number 3 is negative, what does that mean?
2. 10 000 is positive, what does that mean?
3. just sub in values for x?
4. do you know how to maximize functions? you could take the derivativeof the profit function and set that equal to 0, solve for x.

 

[Someone2841]

Annual profit in thousands of dollars is given by the function, P(x) = 200√ x - 3 + 10,000, where x is the number of items sold in thousands, x ≥ 3.

1.describe the meaning of the number 3 in the formula, in terms of its meaning in relation to the profit.
2.describe the meaning of the number 10,000 in the formula, in terms of its meaning in relation to the profit.
3.find the profit for 5 different values of x
4.will this profit function have a maximum, if so, what is it?
5.what steps should the company take to prepare for your answer to part 5?

The formula:

\(\displaystyle P(x) = 200\sqrt{x-3} + 10,000, x \ge 3\)

1. Abstractly, it means that this equation only begins to be useful at \(\displaystyle x=3\).

2. It is the base profit. That is, at \(\displaystyle x=3\), the profit will be 10,000.

3. Example: \(\displaystyle P(3) = 200\sqrt{3-3} + 10,000 = 10,000\)

4. Find \(\displaystyle P'(x) = 0\)

\(\displaystyle P'(x) = 200\frac{1}{2\sqrt{x-3}}, x > 3\)

\(\displaystyle 200\frac{1}{2\sqrt{x-3}} = 0\) has no solution, and therefore no maximum exists.

5. I don't understand the question