# Solve the linear programming problem

• Jul 10th 2010, 10:23 AM
RBlax
Solve the linear programming problem
Assume $x >= 0$ and $y >= 0$

Minimize $C=4x+2y$ with the constraints.

${ x+y>=7, 4x+3y>=4, x<=10, y<=10 }$

So, the minimum is 10, now what ! lol
• Jul 10th 2010, 11:16 AM
earboth
Quote:

Originally Posted by RBlax
Assume $x >= 0$ and $y >= 0$

Minimize $C=4x+2y$ with the constraints.

${ x+y>=7, 4x+3y>=4, x<=10, y<=10 }$

So, the minimum is 10, now what ! lol

1. Re-write the equations (if possible) such that the y-variable is at the LHS of the inequality:

$x\geq0~\wedge~y\geq0$

$y\geq -x+7~\wedge~y\geq-\frac43 x + \frac43~\wedge~x\leq10~\wedge~y\leq10$

2. Draw the corresponding lines which are the borders of the feasible region.

3. The line $y=-2x+\frac12 C$ must contain at least one point of the feasible region and the value of C must be a minimum.

4. According to the sketch you see that

$7=\frac12 C ~\implies~C = 14$

5. To get an exact result calculate the coordinates of the vertices of the feasible region and check which vertex produces the minimum value of C.