Using linear programming, the maximum value of f = 60x + 50y is of 1800 at x = 30 and y = 0.
<h3>How to maximize a function given it's constraints?</h3>
To maximize the function, we have to find the numeric values at the intercepts of the constraints, as the maximum value is the highest numeric value.
In the context of this problem, the function is:
f = 60x + 50y.
Considering the first constraint as an equality, we have that:
5x + 2y = 54.
The intercepts are:
- (0, 27), as 2y = 54, y = 27.
- (10.8, 0), as 5x = 54, x = 10.8.
The second constraint is considered as:
2x + 4y = 60.
The intercepts are:
- (0, 15), as 4y = 60, y = 15.
- (30,0), as 2x = 60, x = 30.
All these intercepts respect the last two constraints, of x and y non-negative.
Then the numeric values at these intercepts are given as follows:
- f(0, 27) = 60(0) + 50(27) = 1350.
- f(10.8,0) = 60(10.8) + 50(0) = 648.
- f(0, 15) = 60(0) + 50(15) = 750.
- f(30,0) = 60(30) + 50(0) = 1800.
Then the maximum value of f = 60x + 50y is of 1800 at x = 30 and y = 0.
More can be learned about linear programming at brainly.com/question/14309521
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