Optimization Promblems?
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04-10-2014, 03:33 PM
Post: #1
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Optimization Promblems?
A fence is to be built to enclose a rectangular area of 290 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
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04-10-2014, 03:39 PM
Post: #2
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Sides should be 10.12 ft x 28.66 ft
Once side of 10.12 ft can be constructed with costly material , and cost will be minimum. Lets say sides of fence be L & B. Area = L * B = 290 Thus L = 290/B Cost = 3L+3L+3B+14B = 6L + 17B = 6*290/B + 17B = 1740*B^-1 + 17B This is cost expressed in therms of B For cost to be min/max derivative of this should be zero. d/dB ( 1740*B^-1 + 17B ) = 0 -1740*B^-2 + 17 = 0 B = sqrt (1740/17) = 10.1169630 L = 290/B = 28.664728 Ads |
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