*The sum of 6 times the length of a shed. It width is 60ft. What are dimensions that gives maximum area for floor of the shed?
To find the dimensions that give the maximum area for the floor of the shed, we need to understand the given information and use some calculus.
Let's define the length of the shed as "l" and the width as 60ft.
The area of the shed's floor is given by the formula: A = length × width.
Given that the sum of 6 times the length of the shed is not specified, we can write this as an equation: 6l.
So, the area of the shed's floor can be written as: A = 6l × 60.
To find the maximum area, we need to find the value of "l" that maximizes this function. We can do this by taking the derivative of A with respect to l, setting it equal to zero, and solving for l.
First, let's rewrite the formula in terms of a single variable (l): A = 360l.
Now, let's differentiate A with respect to l: dA/dl = 360.
Setting the derivative equal to zero, we get: 360 = 0.
This equation has no solution since 360 is not equal to zero. Therefore, there is no maximum area for the floor of the shed.
In other words, the shed can have any length, and its area will increase with the length, but there is no specific value of length that will give the maximum area for the floor of the shed.