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{"ops":[{"attributes":{"bold":true},"insert":"Consider the following product mix problem:"},{"insert":"\n\u00a0\n"},{"attributes":{"bold":true},"insert":"Three machine shops A, B, C produces three types of products X, Y, Z respectively. Each product involves operation of each of the machine shops. The time required for each operation on various products is given as follows:"},{"insert":"\n\n\u00a0\n  \u00a0\n "},{"attributes":{"bold":true},"insert":"Machine shops"},{"insert":"\n \u00a0\n   "},{"attributes":{"bold":true},"insert":"Products"},{"insert":"\n \u00a0\n "},{"attributes":{"bold":true},"insert":"A"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"B"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"C"},{"insert":"\n \u00a0\n "},{"attributes":{"bold":true},"insert":"Profit per unit"},{"insert":"\n   "},{"attributes":{"bold":true},"insert":"X"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"10"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"7"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"2"},{"insert":"\n \u00a0\n "},{"attributes":{"bold":true},"insert":"Birr 12"},{"insert":"\n   "},{"attributes":{"bold":true},"insert":"Y"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"2"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"3"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"4"},{"insert":"\n \u00a0\n "},{"attributes":{"bold":true},"insert":"Birr 3"},{"insert":"\n   "},{"attributes":{"bold":true},"insert":"Z"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"1"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"2"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"1"},{"insert":"\n \u00a0\n "},{"attributes":{"bold":true},"insert":"Birr 1"},{"insert":"\n   "},{"attributes":{"bold":true},"insert":"Available Hours"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"100"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"77"},{"insert":"\n "},{"attributes":{"bold":true},"insert":"80"},{"insert":"\n \u00a0\n  "},{"attributes":{"bold":true},"insert":"Make the Mathematical model of the above primal problem to maximise the profit and then make the dual problem"},{"insert":"\n"}]}

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