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:
Answer:
Part 1)
Part 2)
Part 3)
Part 4)
Part 5)
Part 6)
Step-by-step explanation:
Part 1) we know that
The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle
The area of rectangle is equal to
where
b is the base of rectangle
h is the height of rectangle
so
Part 2) we know that
The shaded region is equal to the area of the complete rectangle minus the area of the interior square
The area of square is equal to
where
b is the length side of the square
so
Part 3) we know that
The area of the shaded region is equal to the area of four rectangles plus the area of one square
so
Part 4) we know that
The shaded region is equal to the area of the complete square minus the area of the interior square
so
Part 5) we know that
The area of the shaded region is equal to the area of triangle minus the area of rectangle
The area of triangle is equal to
where
b is the base of triangle
h is the height of triangle
so
Part 6) we know that
The area of the shaded region is equal to the area of the circle minus the area of rectangle
The area of the circle is equal to
where
r is the radius of the circle
so