<span>A rancher wants to create two rectangular pens, as shown in the attached figure
Let the side parallel to the </span><span>existing fence line = y
And the sides which is perpendicular to </span><span>existing fence line = x
</span><span>The pens need to have a total area of 972 square feet
</span>∴ x y = 972
∴ y = 972/x
Let the length of needed fence = L
∴ L = y + 3x
substituting with the value of y
∴
differentiating the length with respect to x and equating with zero
∴
solve for x
∴ x = 18
substituting to find y
∴ y = 54
<span>The dimensions should be used to minimize the amount of fence used
is 18 , 54 feet </span>
Let the side parallel to the </span><span>existing fence line = y
And the sides which is perpendicular to </span><span>existing fence line = x
</span><span>The pens need to have a total area of 972 square feet
</span>∴ x y = 972
∴ y = 972/x
Let the length of needed fence = L
∴ L = y + 3x
substituting with the value of y
∴
differentiating the length with respect to x and equating with zero
∴
solve for x
∴ x = 18
substituting to find y
∴ y = 54
<span>The dimensions should be used to minimize the amount of fence used
is 18 , 54 feet </span>