a manufacturer makes two types of rubber, butadiene and polyisoprene. the plant has two machines, machine-1 and machine-2, which are used to make the rubber strips. manufacturing one strip of butadiene requires 2.75 hours on machine-1 and 3 hours on machine-2. processing one strip of polyisoprene takes 3.5 hours on machine-1 and 4 hours on machine-2. machine-1 is available 180 hours per month, and machine-2 is available 200 hours per month. formulate an all-integer mathematical model that will determine how many units of each type of rubber should be produced to maximize profits if the profit contributions of butadiene and polyisoprene are $20 and $26, respectively.