• Nov 21st 2009, 05:14 PM
jhonwashington
Hello.

Maximize:
F = 7x + 10y subject to:
14x -5y ≥ 98
8x + 10y ≥ 100

thanks.
• Nov 21st 2009, 11:38 PM
Chris L T521
Quote:

Originally Posted by jhonwashington
Hello.

Maximize:
F = 7x + 10y subject to:
14x -5y ≥ 98
8x + 10y ≥ 100

thanks.

You can create the tableau

$\displaystyle \begin{array}{|c| c c c c | c|}\hline \phantom{x} & x & y & s_1 & s_2 & \phantom{x}\\\hline s_1 & -14 & 5 & 1 & 0 & -98\\ s_2 & -8 & -10 & 0 & 1 & -100\\\hline \phantom{x} & -7 & -10 & 0 & 0 & 0\\\hline \end{array}$

and then apply the dual simplex method.

If you're not familiar with this method, you can introduce slack variables and artifical variables to create a different tableau (which I leave for you to set up). Then use the two phase method to solve the LP problem.

Does this make sense? Can you take it from here?
• Nov 22nd 2009, 03:22 AM
HallsofIvy
Quote:

Originally Posted by jhonwashington
Hello.

Maximize:
F = 7x + 10y subject to:
14x -5y ≥ 98
8x + 10y ≥ 100

thanks.

There is no maximum. You can take x and y are large as you like and so have F as large as you like. Are you sure the conditions are not $\displaystyle 14x- 5y\le 98$ and $\displaystyle 8x+10y\le 100$?
If so:

For a problem with only two variables, it is not necessary to use the tableau method.

Draw the lines 14x- 5y= 98 and 8x+ 10y= 100. Those, together with the condition that neither x nor y is negative, define the "feasible region"- the possible values for x and y. The fundamental theorem of "linear programming" is that the max or min of a linear object function, assuming there is one, must occur at a vertex of the feasible region. The vertices will be where the lines intersect and where they intersect the axes. find the (x,y) coordinates of those points and evaluate 7x+ 10y at those points.
• Nov 22nd 2009, 04:03 AM
mosta86
this equations dont need the simplix method you can solve it easly yousing the graphing method