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

Question

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()

Answer 1

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

Answer 2

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