Hi, these question was given by our doctor as a homework the course is operation research and this chapter is

4. Consider the following linear programming problems:A.B.Min 4x + 3x2 + 6.x3Max5x1 + 5x2 + 24x3S.C.s.t.1x, +05x, + 1x, 2: 1515x1 + 4x2 + 12x3 - 28002x2 + 1x, 2: 3015x) + 8x2$ 60001x, + 1x, + 2x3 = 20+ 8x3 = 1200XXX20For each model:a. Write the dual problem.b. Solve the dual for problem A and the primal problem for B.c. Use the dual solution to identify the optimal solution to the original primal problem forA and the contrary for B.d. Verify that the optimal values for the primal and dual problems are equal.