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Q1.
Which of the following is NOT required for using Newton’s method for
optimization?
The lower
bound for search region.
Twice
differentiable optimization function.
The
function to be optimized.
A good
initial estimate that is reasonably close to the optimal.
Q2.
Which of the following statements is INCORRECT?
If the
second derivative at xi is
negative, then xi
is a maximum.
If the
first derivative at
xi
is zero, then
xi
is an optimum.
If
xi
is a minimum, then the second derivative at xi
is
positive
The value
of the function can be positive or negative as any optima.
Q3. For
what value of x,
is the function x2-2x-6minimized?
0
1
5
3
Q4. We
need to enclose a field with a fence. We have 500 feet of fencing
material with a building on one side of the field where we will not need
any fencing. Determine the maximum area of the field that can be
enclosed by the fence.
x=125,
y=250
x=150,
y=200
x=125,
y=100
x=200,
y=150
Q5. A
rectangular box with a square base and no top has a volume of 500 cubic
inches. Find the length,
l
of the edge of the square base and height,
h
for the box that requires the least amount of material to build. Conduct
two iterations using an initial guess of l=5 in
Base edge
length is 10.00 and height is 5.00
Base edge
length is 9.17 and height is 6.00
Base edge length is 9.00 and height
is 6.17
Base edge length is 10.00 and height
is 10.00
Q6. A
rectangular box with a square base with no top has a surface area of 108
ft2. Find the dimensions that will maximize the
volume. Conduct two iterations using an initial guess of l=3 ft
Base edge
length is 4.15 and height is 4.85
Base edge
length is 6.15 and height is 2.85
Base edge
length is 6.00 and height is 3.00
Base edge
length is 3.85 and height is 6.15
Complete Solution
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