Question

Annual profit in thousands of dollars is given by the function, P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ≥ 0.

describe the meaning of the number -.1 in the formula, in terms of its meaning in relation to the profit.
describe the meaning of the number -300 in the formula, in terms of its meaning in relation to the profit.
find the profit for 5 different values of x

Answer 1

Dillon,

The -.1 is like an efficiency measure. So, there is a particular value that the company can make that will maximize profits.

The graph of the equation is here: http://www.wolframalpha.com/input/?i=plot+-.1x2+%2B+50x+-+300

If you think about the value 300 in relation to P(x). For P(x) to be positive it means that (-1x^2+50x) > 300 will produce a positive value and therefore a profit (not a loss).

To do the last part, just pick 5 values of x, say (100, 200, 300, 400, 500) and find P(x) by plugging in those values.