Question

Annual profit in thousands of dollars is given by the function, P(x) = 100√ x - 5 + 3,000, where x is the number of items sold in thousands, x ≥ 5.

1.describe the meaning of the number 5 in the formula, in terms of its meaning in relation to the profit.
2.describe the meaning of the number 3000 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?

Answer 1

1. if x<5, function is invalid since you cant have the square root of a negative number

2. 3000 is in place to shift the value of P

3. if x = 5, P(x) = 3000
x = 6 , P(x) = 3100
x = 9, P(x) = 3200
x = 14, p(x) = 3300
x = 21, p(x) = 3400

4. for max/min p'(x) = 0
p(x) = 100(x-5)^1/2 + 3000
p'(x) = 100 * 1/2 *(x-5)^-1/2
= 50/√(x-5) (which cannot = 0)
hence no maximum

5. company should sell as many items as possibly to make the most money.

Answer 2

On #4. p(x) = 100(x-5) is the (^) <---- meaning to the 2power? and also is the 1/2 meaning one half?