Question

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.

Answer 1

The all-integer model that determines how many units of each type of rubber should be produced to maximize profits is given by:

• Maximize: P(x,y) = 20x + 26y.

• Constraint 1: 2.75x + 3.5y ≤ 180.

• Constraint 2: 3x + 4y ≤ 200.

• Constraint 3: x ≥ 0, y ≥ 0.

How to maximize profit?

The profit is maximized using linear programming, for a system of equalities/inequalities, in which the variables are given as follows:

• Variable x: number of units of butadiene produced.

• Variable y: number of units of polyisoprene produced.

The profit contributions of butadiene and polyisoprene are $20 and $26, hence the profit function is defined as follows:

P(x,y) = 20x + 26y.

The number of units is a countable amount, hence the values of x and y should be positive, and the constraint is of:

x ≥ 0, y ≥ 0.

Machine-1 is available 180 hours per month, hence the constraint relative to machine-1, considering the time needed for each unit, is of:

2.75x + 3.5y ≤ 180.

Machine-2 is available 200 hours per month, hence the constraint relative to machine-2, considering the time needed for each unit, is of:

3x + 4y ≤ 200.

More can be learned about linear programming at brainly.com/question/14309521

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