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Optimization Promblems? - luca - 04-10-2014 03:33 PM
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.
- girish - 04-10-2014 03:39 PM
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