Business administration club has a budget of 180 OMR to invest into two types of items: A and B. The cost of item A is 11 OMR while the cost of item B is 5 OMR. The club store is only enough for 20 pieces. The profit of selling item A is 4 OMR whereas the profit of selling item B is 2 OMR. How many pieces of each type of items should be purchased in order to maximize the profit? Formulate the problem as a linear programming problem.

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