Using simplex method, maximize z=5x+3ysubject to 2x + y ≤40; x+2y≤50; x, y ≥0101521

Soln:

Or, 3x1 – x2 + x3 = 2 …(i)

Or, - 15x1 + 6x2 – 5x3 = 5 …(ii)

Or, 5x1 – 2x2 + 2x3 = 1 …(iii),

Multiplying equation (i) by 5 and adding with (ii),

Or, x2 = 15 ….(iv)

Multiplying equation (i) by 5 and (iii) by 3 and subtracting (iii) from (i),

Or, x2 + x3 = 7….(v)

Now, we have three equations,

Or, 3x1 – x2 + x3 = 2 …(i)

Or, x2 = 15 …(iv)

Or, x2 – x3 = 7 …(v)

From (iv), we have, x2 = 15.

Using x2 = 15 in (v), we have, x3 = 8.

Using x2 = 15, x3 = 8 in equation (i), we have, x1 = 3.

So, x1 = 3, x2 = 15, x3 =...

Soln:

We have,

Or, x1 + x2 + x3 = -3 …(i)

Or, 3x1 + x2 – 2x3 = -2 …(ii)

Or, 2x1 + 4x2 + 7x3 = 7 …(iii)

Multiplying equation (I) by 3 and subtracting (ii) from (i),

Or, 2x2 + 5x3 = 7 ….(iv)

Multiplying equation (i) by 2 and subtracting (iii) from (i),

Or, -2x2 – 5x3 = 13 …(v)

Adding equation (iv) and (v),

0 = 20.

Now, we have the following three equations.

Or, x1 + x2 + x3 = -3….(i)

Or, 2x2 + 5x3 = 7 ….(iv)

Or, 0.x3 = 20 ….(vi)

Hence, no value of x3 satisfies the equation (vi),

So, the system has no solution....

Soln:

Or, x1 + 2x2 + 3x3 = 4 …(i)

Or, 4x1 + 5x2 + 6x3 = -7 ….(ii)

Or, 7x1 + 8x2 + 9x3 = 10 …… (iii)

Multiplying equation (i) by 4 and then subtracting from (ii),

Or, -3x1 – 6x3 = -23 ….(iv).

Again, multiplying equation (i) by 7 and then subtracting from (iii),

Or, - 6x2 – 12x3 = -18….(v)

Multiplying equation (iv) by 2 and then subtracting from (v),

0 = 28 …(vi)

Now, we have the following equations,

Or, x1 + 2x2 + 3x3 = 4….(i)

Or, - 3x2 – 6x3 = -23 …(iv)

Or, 0.x3 = 28 ….(vi).

No value of x3 satisfies...