SOLUTION: Annual profit in thousands of dollars is given by the function, P(x) = 100*sqrt(x - 5) + 3000. X is the number of items sold in thousands.
a) describe the meaning of the number
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a) describe the meaning of the number
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Question 431987: Annual profit in thousands of dollars is given by the function, P(x) = 100*sqrt(x - 5) + 3000. X is the number of items sold in thousands.
a) describe the meaning of the number 5 in the formula
b) describe the meaning of the number 3000 in the formula
c) find the profit for 5 different values of x
e) will this profit function have a maximum, if so, what is it?
f) what steps should the company take to prepare your the answer in part e. Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! a) The number 5 means that profit function is only valid if a minimum of 5000 items are sold.
b) 3000 is the minimum amount of profit
c) x P(x)
5 3000
6 3100
9 3200
14 3300
21 3400
e) The function will have a maximum if dP(x)/dx = 0
dP/dx = 50/sqrt(x-5) = 0
For finite values of x, this function can never equal zero. Therefore, there is no maximum profit.
f) Maximize profit by selling the most units.
The graph of the function:
