Distinguishing the basic features and characteristics of a dynamic programming problem.

Use the method of Lagrange an multipliers to solve the following NLPP. Does the solution maximize or minimize the objective function? Optimize                 Z = 2x12+ x22+3x32+10x1+8x2+6x3-100 Subject to                x1+x2+x3 = 20 x1, x2, x3 ≥ 0

Write the Kuhn-Tucker conditions for the following problems and obtain the optimal solution: Minimize Z= 2×1+3×2-x12- 2×22 Subject to x1+3×2 ≤ 6, 5×1+2×2 ≤ 10, x1, x2≥ 0

Solve the following quadratic programming problem(Wolf’s method) Maximize         Z = 15x1+30x2+4x1x2-2x12-4x22 Subject to          x1+2x2 ≤ 30, x1,x2≥ 0