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A company manufacturing three different products (P1, P2, P3) uses three assembly lines (A1, A2,A3) for production. Pl is produced in A1, P2 is produced in A2 and P3 is produced in A3. The company makes $2 profit out of one unit of P1, 54 profit out of one unit of P2 and 56 profit out of one unit of P3.The setup costs for A1, A2 and A3 are $300, 5500 and $900 respectively and paid only if the associated line is used. 3 units of raw material are needed to manufacture one unit of P1, 5 units of raw material are needed to manufacture one unit of P2 and 7 units of raw material are needed to manufacture one unit of P3. A total of 4200 units of raw material are available. Define your decision variables and formulate an IP to maximize company's profits with following additional restrictions. If A1 is opened, then A2 must be opened. Either A1 or A2 must be opened. At least two assembly line must be opened