Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100

Question

Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x is the number of items sold in thousands, x = 10.

describe the meaning of the number 12 in the formula
describe the meaning of the number -100 in the formula
find the profit for 5 different values of x
graph the profit function over its given domain; use the 5 values calculated in part 3 to construct the graph and connect these points with a straight line in Excel or another graphing utility. Insert the graph in a Word file and attach the graph in a Word file to the class DB thread.
will this profit function have a maximum, if so, what is it?
what steps should the company take to prepare for your answer to part 5?

Explanation / Answer

I'm not completely sure how to put a graph in, but I can give you the data. A. The number 12 in the function indicates the slope of the line. This basically says for every time you increase x by one, y [or P(x)] increases by 12. B. The number -100 is the y-intercept. When x=0, the profit is -100. C. Here are 5 values: P(5) = 12(5)-100 = -40 P(8) = 12(8)-100 = -4 P(10) = 12(10)-100 = 20 P(12) = 12(12)-100 = 44 P(15) = 12(15)-100 = 110 D. There is no maximum for this function, because the graph is a straight line.

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