1 Solve the following linear programming problem using graphical methods. Find 1 and 22 to maximise 21 +222 subject to the constraints #1 + 6x2 12 321+522 15 #1 20, 22 20 2 Repeat question 1 in the case where a) the objective function becomes 2x1 + x2 b) the constraints become -1 +62 12 -3x1 +5x2 15 21 0,2 20 with the original objective function. 3 Solve the following linear programming problem using graphical methods. Find y and 32 to minimise 3 +32 subject to the constraints 9/1 + 232 23 23/1+1/2 25 3/2 20 4 Maximise az+z2 subject to the constraints 4x1 + 2x2 12 -#1+ 1 #1 + 2x 4 21 0,72 20 Find the value as a function of a. 5 Repeat question 1 using the simplex method in two dimensions and confirm that you get the same result. 6 Repeat question 3 using the simplex method in two dimensions and confirm that you get the same result.