A machine is used in three adjusted modes to produce three products: Product A, B and C. In the first mode the daily capacity of the machine can produce at most 17 units of product A and 31 units of product B and 18 units of product C. In the second mode, the machine can be adjusted to produce at most 21 units of product 1 and 16 units of product 2 and 13 units of product C daily. In the third mode, the machine can be adjusted to produce at most 13 units of product 1 and 26 units of product 2 and at least 31 units of product C daily. Market analysis shows that the maximum daily demand for product A and B combined is 37 units. It was also indicated that there was a requirement to produce at least three units of product A and two units of product B for each units of product C. If the whole labor force is engaged in only producing product-A, time will permit 50 units of product A to be produced. Labor time to manufacture product A is twice that for product B and thrice that for product C. Given that the unit profits for product A, B and C are $20, $22, and $21 respectively, formulate a mathematical programming model to determine that which of the machine setting should be selected.