Question: Consider the following LP problem, which will be called LP1. min w = -10x1 + 25.2 s.t. 921 + 12 > 18 3x + 2x2

Consider the following LP problem, which will be called LP1. min w = -10x1 + 25.2 s.t. 921 + 12 > 18 3x + 2x2 32 21,220 (a) Convert LP1 into a maximization problem, then solve it graphically. Remember to show all constraints and to calculate, not guess, the solution from the graph. Also remember that the original problem is a minimization problem. (10 marks) (b) Solve the maximization problem using the Simplex Method as explained in the study book, showing all completed tableaux. (10 marks) (c) Write down the standard form of the primal and then the dual form (denoted by LP2) of the maximization problem LP1 in (a). (8 marks) (a) Using your solution to part (a) (do not use Simplex!), determine the optimal solution to LP2. Explain how you deduced this solution. (7 marks) (e) Using the final tableau from part (b), determine the optimal solution to LP2. Explain how you deduced this solution. (5 marks) Note: You are to solve this problem manually, with full working shown, but you may use software to check your results

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