For the following problem, add a squared slack variable, , to the first constraint to prod...

For the following problem, add a squared slack variable, , to the first constraint to produce an equation.

(a) Solve the optimization problem using calculus with substitution (ultimately a problem in one variable).

(b) For the answer found, derive the sufficiency condition and state the type of critical point.

(c) From the form of the revised objective function, is the critical point a global optimum? If so, what type?

Optimize Z = 4x1x2+ x1

Subject to: x1 ≤ 5

x1 + x2 = 2