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A decorative item dealer deals in two items A and B. He has  15,000 to invest and a space to store at the most 80 pieces. Item A costs him 300 and item B costs him 150. He can sell items A and B at respective profits of  50 and  28. Assuming he can sell all that he buys, formulate the linear programming problem in order to maximize his profit and solve it graphically.

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Let x be the number of pieces of item A and y be the number of pieces of item B.

The feasible shaded region (OABC) is shown in graph, then four points O, A, B and C are critical points. Substituting the values of these points in profit equation, we get 

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