# Question: Consider the following nonlinear programming problem Minimize Z x41

Consider the following nonlinear programming problem:

Minimize Z = x41 + 2x21 + 2x1 x2 + 4x22,

Subject to

and

x1 ≥ 0, x2 ≥ 0.

(a) Of the special types of nonlinear programming problems described in Sec. 13.3, to which type or types can this particular problem be fitted? Justify your answer.

(b) Now suppose that the problem is changed slightly by replacing the nonnegativity constraints by x1 ≥ 1 and x2 ≥ 1. Convert this new problem to an equivalent problem that has just two functional constraints, two variables, and two nonnegativity constraints.

Minimize Z = x41 + 2x21 + 2x1 x2 + 4x22,

Subject to

and

x1 ≥ 0, x2 ≥ 0.

(a) Of the special types of nonlinear programming problems described in Sec. 13.3, to which type or types can this particular problem be fitted? Justify your answer.

(b) Now suppose that the problem is changed slightly by replacing the nonnegativity constraints by x1 ≥ 1 and x2 ≥ 1. Convert this new problem to an equivalent problem that has just two functional constraints, two variables, and two nonnegativity constraints.

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