Consider the following LP model: Minimise -7r + 2y subject to 7r + 3y > 27 -r+4y > 5 7x - 2y $ 43 and I,y 2 0. (4.1) Represent all the constraints of the LP model on a graph. Represent I on the horizontal axis and y on the vertical axis. Label all relevant lines on the graph and indicate the feasible region clearly. (6) Important note: Use the necessary tools to draw a reasonably accurate graph. A rough sketch is not acceptable. (4.2) Find all the corner points of the feasible region and evaluate the objective function at each of them. (3) (4.3) Deduce the optimal solution. If the LP problem is infeasible or unbounded, give the reason for this. If the LP problem has multiple optimal solutions, find the general optimal solution. (4) (4.4) State clearly all redundant, binding and nonbinding constraints in this linear programming problem. (3) (4.5) Find the shadow prices for each binding constraint of this LP model. (3) Definition: The shadow price is the amount of change in the objective function value per unit increase on the right-hand side of a functional constraint