# Math Help - Please help me to solve the followings linear programming problems. Thanks.

1. ## Please help me to solve the followings linear programming problems. Thanks.

Hello.
could somebody please help me to solve this exercise?

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

thanks.

2. Originally Posted by jhonwashington
Hello.
could somebody please help me to solve this exercise?

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

thanks.
You can create the tableau

$
\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?

3. Originally Posted by jhonwashington
Hello.
could somebody please help me to solve this exercise?

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 $14x- 5y\le 98$ and $8x+10y\le 100$?
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.

4. this equations dont need the simplix method you can solve it easly yousing the graphing method