Question

Construct the dual problem associated with the primal problem. Solve the primal problem. Minimize C = 10x + y subject to 4x + y greaterthanorequalto 23 x + 2y greaterthanorequalto 19 x greaterthanorequalto 2 x greaterthanorequalto 0, y greaterthanorequalto 0 The minimum is C = at (x, y) =

Answer 1

To construct the dual problem, convert the minimization problem to a maximization problem. Solve the primal problem using optimization techniques to find the minimum value of the objective function C.

Step-by-step explanation:

To construct the dual problem associated with the given primal problem, we need to convert the minimization problem into a maximization problem. In the dual problem, the coefficients of the variables in the objective function become the constraints, and vice versa.

The dual problem for the given primal problem is:

Maximize D = 23a + 19b + 2c + 0d

subject to:

4a + b + d ≤ 10

a + 2b + d ≤ 1

a, b, c, d ≥ 0

To solve the primal problem, we can use various optimization techniques such as the Simplex method or graphical method to find the minimum value of the objective function C. Once we solve the primal problem, we can substitute the values of x and y into the objective function C to determine the minimum value.

By applying the chosen method, we find that the minimum value of C occurs when x = 2.5 and y = 20.5. Therefore, the minimum value of C is 10(2.5) + 20.5 = 30.