Question 613258
Since profit = revenue - cost, let's make a profit function, P(x) that will be R(x) - C(x):
{{{P(x) = R(x) - C(x) = (55x - 2x^2) - (21x + 98)}}}
Note the use of parentheses! Without them we would not realize that both the 21 and the 98 should be subtracted.
{{{P(x) = R(x) - C(x) = (55x - 2x^2) - (21x + 98) = -2x^2 + 34x -98}}}<br>
Now that we have our profit function, we can see that:<ul><li>Its graph will be a parabola because of the squared term.</li><li>The parabola will open downward because of the negative coefficient, -2, in front of the squared term.</li><li>The highest point (which would be the maximum profit) on the downward parabola would be the vertex of the parabola.</LI></ul>From the above we now know that we want to find the vertex of the profit parabola.<br>
The x coordinate of the vertex of a parabola will be -b/2a where the "b" is the coefficient of the x term and the "a" is the coefficient of the x squared term. From
{{{P(x) = -2x^2 + 34x -98}}}<br>
we can see that your "a" is -2 and your "b" is 34. So the x coordinate of the vertex (which is where the maximum profit is) will be:
{{{-34/(-2) = 17}}}