help me solve these 2 questions. each question has 3 sub questions (a),(b) and (c)
Consider the constraints y≤−2x+4,y−2x≤3,y+1≥2x,x,y≥0. (a) Plot the constraints and shade the feasible region. In your plot, label each line which forms the boundary of the feasible region. (b) Write the feasible region in matrix-vector form Ax≤b,x≥0. (c) Find all vertices of the feasible region.
In this question we will use the method of slack variables to find the vertices of the feasible region defined by the inequalities 2x1+x22x1+3x2x1,x2≤4≤6≥0 (a) Write down the linear system obtained from this system of inequalities by adding non-negative slack variables. (b) Use Gauss-Jordan elimination to find the basic solutions corresponding to the basic variables: (i) x3,x4; (ii) x2,x4; (iii) x2,x3. (c) The remaining basic solutions are (23,1,0,0),(2,0,0,2) and (3,0,−2,0). Using your answers as well as these, list the vertices of the region.