Given the following LP problem MAX 90A + 84 B + 70 C S.T. 1) 10 A + 8 B + 9 C ≤ 5000 2) 2 A + 3 B + 3 C ≤ 1800 3) 1 A + 1 B + 1 C =600 4) 1C ≥ 150 A , B, C ≥ 0 a) Convert this 3-var LP problem into a 2-var LP problem consisting only of A and B. Show all your workings clearly. b) Using the result from part (ii), and by plotting on a graph paper with B on y-axis and A on x-axis), graphically solve for the optimal solution of the original 3-var LP problem. c) Using sensitivity analysis and/or the graph, determine the dual value for constraint 4 in the original LP problem. Note: do not simply read the dual value directly from the output table.