The whole statement is as follows: When there are 75 things in production, a profit of 10000 dollars is obtained, which is the highest possible.
Because we already know that the profit equation is defined between x = 0 and x = 150, which are the two roots of the equation, we also know that the profit is equal to zero when
x = 0 and when x = 150.
If this is the case, we may reasonably expect a positive return on investment within this range.
Therefore, the quadratic equation should have a leading coefficient that is negative. This would indicate that the arms of the graph should move in a downward direction.
If this is the case, then we already know that the maximum will be located at the vertex of the triangle.
In this case, we are aware that the vertex is:
(75, 10000)
In this equation, x stands for the total number of products sold, while y indicates the amount of money made.
Since the maximum is at the vertex, and we know that the vertex is located at (75, 10000), we may draw the conclusion that the maximum profit is $10000, and this occurs when the number of things created is 75. This is because the vertex is located at the intersection of the two lines.
Therefore, the whole statement is as follows:
When there are 75 things in production, a profit of 10000 dollars is obtained, which is the highest possible.
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