a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen?
a. A rectangular pen is built with one side against a barn. If 200 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 400 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.
The interval of interest of the objective function is(enter your response here).
To maximize the area of the pen, the sides perpendicular to the barn should be (enter your response here)
m long and the side parallel to the barn should be(enter your response here)m long.
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.
The interval of interest of the objective function is (enter your response here).
To minimize the amount of fence that must be used, each of the sides perpendicular to the barn should be(enter your response here)m long and each of the sides parallel to the barn should be(enter your response here)m long.
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