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# Find the dimensions of the enclosure that is most economical to construct.

A fence is to be built to enclose a rectangular area of 250 square feet. The fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 16 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Dimensions= ()x()

### 2 Answers by Expert Tutors

Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
5.0 5.0 (1 lesson ratings) (1)
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Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative
The two equations are:
10a + 21b = min  Target equation.
a*b=250
Objective Cell (Min)
E\$3 458.2574088 458.2574088

Variable Cells
Cell Name Original Value Final Value Integer
\$E\$4 22.901828 22.901828 Contin
\$E\$5 10.91614899 10.91614899 Contin
The answer is: Two sides of 10.91 feet one of which is the costly, and two sides of 22.90 feet with an area equal to 250 sq feet
Total minimum cost will be \$ 458.26 dollars.

Constraints
Cell Name Cell Value Formula Status Slack
\$E\$6 249.9997666 \$E\$6=250 Binding 0

Good way of getting an answer but I think that is very long and tiresome. Anyhow, in my old country they say that "everybody kills fleas on his own way". Is agood answer and checks mine. Thanks.
You're welcome, Francisco. I didn't recognize your solution. I assume it's some type of computer program or something I'm just not familiar with. Anyway, you got the answer the student was looking for. Good solution; right down to the penny.
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
4.8 4.8 (13 lesson ratings) (13)
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250=1x2x5x5x5
Using only integers, find the rectangle with the smallest perimeter:
1X250 gives 502 ft
2x125 gives 254 ft
5x50 gives 110 ft
10x25 gives 70 ft
(25+25+10)*(5)=(60)*(5)=\$300
10*16=\$160
\$300+\$160=\$460
If you use trial and error from here and use 11x(250/11)=11x22.7272...
22.73+22.73+11=56.46
56.46*5=\$282.30
11*16=\$176
\$282.30+\$176=\$458.30
22.73x11=250.03 sq ft