Consider the following nonlinear programming problem.
Maximize Z = x31 + 4x22 + 16x3,
Subject to
x1 x2 x3 =4
and
x1 ≥ 1, x2 ≥ 1, x3 ≥ 1.
(a) Solve by dynamic programming when, in addition to the given constraints, all three variables also are required to be integer.
(b) Use dynamic programming to solve the problem as given (continuous variables).