Answer:
The profit function is:
The maximum value is 406, 300 occurring when x = 640.
Step-by-step explanation:
The revenue function is:
And the cost function is:
Then the total profit function will be:
This is a quadratic function.
Therefore, the maximum value of the total profit will occur at its vertex point.
The vertex of a quadratic is given by:
In this case, a = -1, b = 1280, and c = -3300.
Then the point at which the maximum profit occurs is at:
And the maximum profit will be:
we have
we know that
The area of a rectangle is equal to
where
L is the length side of the rectangle
W is the width side of the rectangle
In this problem
Equate the area to zero and Find the roots of the quadratic equation
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
Square root both sides
so
therefore
<u>the answer is the option</u>
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