Answer:
602/19 = 31 13/19 (see comment)
Explanation:
You want the maximum value of 8x +5y +4z given the constraints:
- 2x+5y+4z ≤ 8
- 2x-3y+5z ≤ 9
- 2x-2y+12z ≥ 10
Solver
A number of solvers are available for linear programming problems. We have shown the result of using one of them in the first attachment.
The maximum objective function value is 602/19 = 31 13/19.
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Additional comment
The usual requirement for linear programming problems is that the variables have non-negative values. We note that the "optimal" solution has a negative value for y. If we restrict the variables to be non-negative, then the maximum objective function value is 29, as shown in the second attachment.
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