4) A farmer wishes to fence in a rectangular pasture on a 3,750 square foot piec

Question

4) A farmer wishes to fence in a rectangular pasture on a 3,750 square foot piece of riverfront property. He also plans to separate the pasture into four regions as shown in my drawing. What is the least amount of fence he will need to buy? Since his cows never learned to swim he will not need to erect a fence along the river. Hints: Before you take a derivative of a function to find its critical numbers, the function has to be in terms of one variable. It could have all x's or all y's but not both.

Explanation / Answer

Clearly the drawing is missing to make any calculation. But I will just try to calculate without that.

Rectangular area = 3750 = x*y

let the area is divided along x into 4 parts.

so each area has length as x/4 and breath as y.

so total fence required is (F) = 5y + 2x

x = 3750/y

F = 5y + 2*3750/y = 5y + 7500/y

first derivative = F' = 5 - 7500/y2 = 0

y^2 = 1500

y = 38.73 feet

x = 96.82

Fence required minimum = 387.30 feet

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.