Question

A farmer has 1000 feet of fencing and wants to enclose a rectangular yard, and divide it into four pens as shown.

a. Find a function A(x) modeling the total area as a function of x, Hint: write the amount of fencing needed
in terms of x and y and set that equal to 1000, then you can solve for y. This should allow you to write
down the area in terms of x alone. Your function should be a quadratic function.

Answer 1

9514 1404 393

Answer:

A(x) = -2/5x^2 +200x

Explanation:

There are 5 lengths of fence that are y long, and 2 lengths of fence that are x long. So, the perimeter is ...

5y +2x = 1000

Then the value of y is ...

y = (1000 -2x)/5

The area is the product of x and y:

A(x) = xy

A(x) = x(1000 -2x)/5

A(x) = (2/5)(x)(500-x) . . . a convenient form for finding the maximum area

In standard form, the equation is ...

A(x) = -2/5x^2 +200x