A rancher wishes to fence in a rectangular corral enclosing 1300 square yards and must divide it in half with a fence down the middle. If the perimeter fence costs $5 per yard and the fence down the middle costs $3 per yard, determine the dimensions of the corral so that the fencing cost will be as small as possible.
A) $10 \sqrt { 10 } \times 13 \sqrt { 10 }$

B) $13 \sqrt { 10 } \times 13 \sqrt { 10 }$
C) $10 \sqrt { 13 } \times 13 \sqrt { 13 }$
D) $10 \times 10$
E) $10 \sqrt { 10 } \times 10 \sqrt { 10 }$

F) $10 \sqrt { 13 } \times 10 \sqrt { 13 }$.

G) $13 \times 13$

Question

A rancher wishes to fence in a rectangular corral enclosing 1300 square yards and must divide it in half with a fence down the middle. If the perimeter fence costs $5 per yard and the fence down the middle costs $3 per yard, determine the dimensions of the corral so that the fencing cost will be as small as possible.
A) $10 \sqrt { 10 } \times 13 \sqrt { 10 }$

B) $13 \sqrt { 10 } \times 13 \sqrt { 10 }$
C) $10 \sqrt { 13 } \times 13 \sqrt { 13 }$
D) $10 \times 10$
E) $10 \sqrt { 10 } \times 10 \sqrt { 10 }$
 
F) $10 \sqrt { 13 } \times 10 \sqrt { 13 }$.

G) $13 \times 13$

Quizplus · Accepted Answer

The cost of fencing is minimized when the corral is a square, but since it's divided in half, the optimal shape is a double square (two squares side by side), making the dimensions $10 \sqrt { 10 } \times 13 \sqrt { 10 }$ to enclose 1300 square yards with minimum fencing cost.

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A Rancher Wishes to Fence in a Rectangular Corral Enclosing $10 \sqrt { 10 } \times 13 \sqrt { 10 }$