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 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? the interval of interest of the objective function is (0,850. (simplify your answer. type your answer in interval notation. do not use commas in the individual endpoints.) to maximize the area of the pen, the sides perpendicular to the barn should be 425 m long and the side parallel to the barn should be 850 m. b. let x be the length of the sides perpendicular to the barn and let l be the total length of fence needed. write the objective function. l = (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 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? the interval of interest of the objective function is (0,850. (simplify your answer. type your answer in interval notation. do not use commas in the individual endpoints.) to maximize the area of the pen, the sides perpendicular to the barn should be 425 m long and the side parallel to the barn should be 850 m. b. let x be the length of the sides perpendicular to the barn and let l be the total length of fence needed. write the objective function. l = (type an expression.)

Answer

Explanation:

Step1: Find area - side relationship

Since each pen has area $A = 25\ m^{2}$ and let the side perpendicular to the barn be $x$, then the side parallel to the barn for each pen is $\frac{25}{x}$.

Step2: Determine total - length of fence

There are 4 adjacent pens. The total length of the sides perpendicular to the barn is $5x$ (5 such sides in total for 4 adjacent pens) and the total length of the sides parallel to the barn is $\frac{25}{x}$. So the objective function for the total length of fence $L$ is $L = 5x+\frac{25}{x}\times4=5x + \frac{100}{x}$.

Answer:

$5x+\frac{100}{x}$