Question: 1. (22 marks) Given the following LP problem. Max kx + ky s.t. 2x + 3y 12 (constraint 2) 7x + 2y s 70 (constraint

1. (22 marks) Given the following LP problem. Max

1. (22 marks) Given the following LP problem. Max kx + ky s.t. 2x + 3y 12 (constraint 2) 7x + 2y s 70 (constraint 3) x,y > 0 where k is a positive constant. (a) Produce a detailed graph of the feasible region. (b) Identify the optimal solution. Justify your answer. (c) Determine the coordinates of the optimal solution by solving system of linear equations. (d) Determine the value of k if the optimal solution value = 130

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