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.
<h3>How to maximize profit?</h3>
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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