(Solved): 1. - [20 points) A machine is used to produce two interchangeable products. There are two possible ...

1. - [20 points) A machine is used to produce two interchangeable products. There are two possible settings of the machine: The daily capacity of the machine can produce at most 20 units of product 1 and at most 10 units of product 2 (M/C setting 1). Alternatively, the machine can be adjusted (M/C setting 2) to produce at most 12 units of product 1 and at most 25 units of product 2 daily. Market analysis shows that the maximum daily demand for the two products combined is 35 units. Given that the unit profits for the two respective products are $10 and $12, which of the two machine settings should be selected? Formulate an appropriate mathematical model (should not be nonlinear!) for the above problem.