How can I solve the following linear program? I want to find the answer for the following linear program.
Max $v$
subject to
$$v-5x_1-x_2 \le 0 $$
$$ v-x_1-4x_2 \le 0 $$
$$ v-2x_1-3x_2 \le 0 $$
$$ x_1+x_2 = 1 $$
$$ x_1, x_2 \ge 0  $$
$$ v \in R $$
I know how to solve following linear program by using MATLAB
$$C^T x$$
$$s.t. Ax \le b  $$
$$x \ge 0$$
We can solve this by the following MATLAB code
[x, fval]=linprog(C, A, b)

How can I solve the above linear program by using MATLAB?
I cannot identify C, A, b matrices and their dimentions in the above problem. 
The answers should be 
$$x_1=0.4, x_2=0.6, v=2.6$$

My second problem is
$$ 3x_1-7x_2 \le y$$
$$ -3x_2-5x_3 \le y$$
$$ -x_1-7x_2 \le y$$
$$x_1+x_2+x_3 =1 $$ 
$$x_1,x_2,x_3 \ge 0 $$ 
 A: The equality constraint can be passed on in the Aeq,beq parameters. I.e.
>> f=[-1,0,0]; A=[1,-5,-1;1,-1,-4;1,-2,-3]; b=[0;0;0]; A2=[0,1,1]; b2=1; lo=[-inf,0,0]; up=[inf,inf,inf];
>> [x,fval]=linprog(f,A,b,A2,b2,lo,up);
Optimization terminated.
>> x

x =

    2.6000
    0.4000
    0.6000

>> fval

fval =

   -2.6000

A: Second answer for extra bonus points.
First note that you first equation looks very suspicious: $−u+3x_2−7x_2≤0$ and does not correspond to the first row in $A$.
Second 1e-12 vs 0 is very close. Within the tolerances. I would be happy with such a result. If you really care about this minuscule differences, solve with dual simplex method:
>> options = optimoptions(@linprog,'Algorithm','dual-simplex');
>> [x, fval]=linprog(f, A, b, A2, b2, lo, up, [], options)

Optimal solution found.


x =

         0
    0.3333
    0.4667
    0.2000


fval =

     0

The second question has been removed by the poster so this answer is now a bit hanging in the air. Not sure what is happening with these bonus points.
