Question

a)Consider the following nonlinear programming problem.
max−4x^2 + |3x − 9| + 3 − x
s.t. x belongs to [−5, 5]
Which of the following is the solution to the nonlinear programming problem? (Explanation Please)
A. x = −5.
B. x = 5.
C. x = −1/2.
D. x = 3.

b)Consider the following nonlinear programming problem.
max x^2 + |2x − 4| + 2 − 3x
s.t. x belongs to [−5, 5]
Which of the following is the set of critical points of the nonlinear programming problem? (Explanation)
A. x = −5, x = 1/2,x=2,x=5
2 , x = 2, x = 5,x=5/2,x=5
B. x = −5, x = 2, x = 5
2 , x = 5.
C. x = −5, x = 1
2 , x = 2, x = 5
2 , x = 5.
D. x = −5, x = 2, x = 5.

c)3. Consider the following quadratic nonlinear program. (Explanation)
max f(x) = -5x^2-3y^2+2xy+4x+6y

s.t. 2x+3y >= 12

i) Determine whether the function f(x) is convex, concave, or neither.

Answer 1

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