Solve the linear programming problem by graphing. graph the feasible region, list the extreme points and identify the maximum value of z. list the equations of the lines that form the feasible region
minimize z=4x+y
subject to
2x+4y> = 20
3x+2y< =24
x, y> =0

The minimum value of objective function is 5 at x=0 and y=5.

Step-by-step explanation:

The given linear programming problem is

Minimize

Subject to  constraints

        .... (1)

         .... (2)

The related line of both inequalities are solid lines because the sign of inequalities are ≤ and ≥. It means the points lie on related line are included in the solution set.

Check both inequalities by (0,0).

This statement is not true. So, the shaded region of inequality (1) will not contain the origin.

This statement is true. It means the shaded region of inequality (2) will contain the origin.

means first quadrant.

The common shaded region is feasible region. The vertices of feasible region are (0,5), (0,12) and (7,1.5).

Calculate the value of objective function at these vertices.

For (0,5)

For (0,12)

For (7,1.5)

Therefore the minimum value of objective function is 5 at x=0 and y=5.

where is the rest of the

step-by-step explanation: