A rectangular field is to be enclosed on four sides with a fence Fencing costs $

Question

A rectangular field is to be enclosed on four sides with a fence   Fencing costs $5 per foot for two opposite sides, and $3 per foot for the two other sides. Find the dimensions of the field of area 690 ft^2 that would be the cheapest to enclose.

This Question: B pts 5 of 14 (8 ca A rectangular field is to be enclosed on four sid for two opposite sides, and $3 per foot for the field of area 690 ft2 that would be the cheapest O A. 15.8 ft $5 by 43 8 ft $3 O B. 43 8 ft $5 by 15.8 ft S3 O C. 339 ft $5 by 20.4 ft $3 O D. 20.4 ft $5 by 339 ft@ $3

Explanation / Answer

Let the length of the field be x ft and breadth be y ft

Given x*y = 690 sq ft

Also 10x + 6y is the total cost.

Total cost = 10x + 6 *690/x

Let f(x) = 10x + 6 *690/x

f(x) is minimum when f'(x) = 0 (f''(x) > 0)

Differentiating, f'(x) = 10 - 4140/x2 = 0

=> x2 = 4140 = 414 => x = 20.4 ft

=> y = 690/20.4 = 30.9 ft

So the minimum cost is

D. 20.4ft @ 5 and 30.9ft@3

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