Francisco E. answered • 06/21/14
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Francisco; Civil Engineering, Math., Science, Spanish, Computers.
Please check the answer that was given to Jessica today about the same problem. Is as follows:
What are the dimensions of such a rectangle with the greatest possible area?
A rectangle has its two lower corners on the x-axis and its two upper corners on the parabola y=9-x2.
What are the dimensions of such a rectangle with the greatest possible area?
1.Width=
2.Height=
This is a parabola that opens vertically, points upward or opens downward and the vertex is located on the Y axis coordinates are:
k=y=9, the vertex is on (0,9), with this data we can work.
The base distance will be equal to 2x at any y less than 9, and the area of the rectangle will be
2x*y = (2*(9-Y)0.5 )*Y
Now we need to maximize this area using solver to make it faster.
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
Objective Cell (Max)
Cell Name Original Value Final Value
$E$3 5.656854249 20.78
A rectangle has its two lower corners on the x-axis and its two upper corners on the parabola y=9-x2.
What are the dimensions of such a rectangle with the greatest possible area?
1.Width=
2.Height=
This is a parabola that opens vertically, points upward or opens downward and the vertex is located on the Y axis coordinates are:
k=y=9, the vertex is on (0,9), with this data we can work.
The base distance will be equal to 2x at any y less than 9, and the area of the rectangle will be
2x*y = (2*(9-Y)0.5 )*Y
Now we need to maximize this area using solver to make it faster.
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
Objective Cell (Max)
Cell Name Original Value Final Value
$E$3 5.656854249 20.78
The answer is: height (Y) = 6 units and then x will be known with the parabola equation, will be X= 3.47
and the area (max) will be 20.78
Variable Cells
Cell Name Original Value Final Value Integer
$E$4 Y 1 5.99999989 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$E$4 Y 5.99999989 $E$4<=9 Not Binding 3.00000011
