the owner of the Laurel Nursery Garden Center wants to fence in 1400 ft^2 of land in a rectangular plot to be used for diﬀerent types of shrubs. The plot is to be divided into six equal plots with fivefe nces parallel to the same pair of sides.
What is the least amount of fence needed?

Question

the owner of the Laurel Nursery Garden Center wants to fence in 1400 ft^2 of land in a rectangular plot to be used for diﬀerent types of shrubs. The plot is to be divided into six equal plots with fivefe nces parallel to the same pair of sides. 
What is the least amount of fence needed?

anonymous · Answer

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anonymous · Answer

Perimeter: $P=x + 7y$
Area: $A = xy = 1400$

Perimeter is what you want to minimize so solve the area equation for x or y.
$$x=\frac{1400}{y}$$

So
$$P=\frac{1400}{y}+7y$$
Take the derivative and set it equal to 0 to find the $y$ where $P$ is minimized, then go back and find the P to get the length of fence.