a. a rectangular pen is built with one side against a barn. if 1700 m of fencing are used for the other…

a. a rectangular pen is built with one side against a barn. if 1700 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. a rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 25 m² (see figure). what are the dimensions of each pen that minimize the amount of fence that must be used? a. let a be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. write the objective function in a form that does not include the length of the side parallel to the barn. a = (type an expression.)

a. a rectangular pen is built with one side against a barn. if 1700 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. a rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 25 m² (see figure). what are the dimensions of each pen that minimize the amount of fence that must be used? a. let a be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. write the objective function in a form that does not include the length of the side parallel to the barn. a = (type an expression.)

Answer

Explanation:

Step1: Define variables

Let $x$ be the length of the sides perpendicular to the barn. The total length of the three - sided fence is 1700 m. So the length of the side parallel to the barn is $1700 - 2x$.

Step2: Write the area formula

The area $A$ of a rectangle is given by the product of its length and width. Here, $A(x)=x(1700 - 2x)=1700x-2x^{2}$.

Answer:

$1700x - 2x^{2}$