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P Take a Test Nicolas Guarisco Google Chrome www.mathxl.com/Student/PlayerTest.aspx?testld 60741510&center; win-yes Nicolas Guarisco 3/31/14 10:36 PM Quiz: Quiz 9 (Section 5.6) 4 of 10 complete This Question: 1 pt This Test: 10 pts Time Remaining: 01:03:34 A fence must be built to enclose a rectangular area of 20,000 ft2. Fencing material costs $3 per foot for the two sides facing north and south and $6 per foot for the other two sides. Find the cost of the least expensive fence. The cost of the least expensive fence is Simplify your answer Vi Vi (u) oo Enter any number or expression in the edit field. Previous Question Next Question Submit Quiz 10:36 PM 3/31/2014

Explanation / Answer

let length be l and breadth be b.

So, lb = 20000

Perimeter = 2(l+b)

Fencing cost for l = $3

Fencing cost for b = $6

So, p = 2(3l+6b)

To minimise this cost,

let l = 20000/b

p = 6(20000/b + 2b)

differentiating with respect to b,

0 = 6(-20000/b^2 +2)

b^2 = 10000

b = 100

l = 200

So, least cost = 2(600 + 600)

=2400$

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