a. a rectangular pen is built with one side against a barn. if 1700 m of fencing is used, what is the…

a. a rectangular pen is built with one side against a barn. if 1700 m of fencing is used, what is the maximum area of the pen? b. a rancher plans to make four identical and adjacent rectangular pens against a barn. 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 and y be the length of the side parallel to the barn. a = 1700x - 2x² (type an expression.) the interval of interest of the objective function is . (simplify your answer. type your answer in interval notation. do not use commas)

a. a rectangular pen is built with one side against a barn. if 1700 m of fencing is used, what is the maximum area of the pen? b. a rancher plans to make four identical and adjacent rectangular pens against a barn. 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 and y be the length of the side parallel to the barn. a = 1700x - 2x² (type an expression.) the interval of interest of the objective function is . (simplify your answer. type your answer in interval notation. do not use commas)

Answer

Explanation:

Step1: Analyze the non - negativity of variables

Since (x) represents the length of a side of the pen, (x\geq0). Also, the total length of the fence is 1700m. If the side parallel to the barn has length (x) and the other two equal - length sides perpendicular to the barn have length (y), then (x + 2y=1700), so (y=\frac{1700 - x}{2}\geq0). Solving (y\geq0) gives (1700−x\geq0) or (x\leq1700).

Step2: Write the interval

The interval of interest for (x) is determined by the non - negativity of the side lengths. The interval of interest of the objective function (A(x)=1700x - 2x^{2}) is ([0,1700]).

Answer:

([0,1700])