Final answer:
The linear programming problem to maximize -3x + 6y with constraints 6x + 3y ≤ -7, 3x - y ≥ -4, x ≥ 0, and y ≥ 0 cannot be directly rewritten in the requested format as one constraint has a negative constant. However, assuming we can multiply by -1 (which changes the problem), the constraint would become -6x - 3y ≥ 7.
Step-by-step explanation:
The task is to rewrite the given linear programming problem as a maximization problem and to reformulate the given inequalities in the specified format.
The maximization objective is to maximize the function -3x + 6y.
The constraints provided are 6x + 3y ≤ -7 and 3x - y ≥ -4, along with x ≥ 0 and y ≥ 0.
To rewrite the first inequality in the required form, we must have the linear expression on the left and the constant on the right.
However, given that 6x + 3y is already smaller than -7, this constraint is not in standard form because the right side should be nonnegative.
Here, since we cannot easily change the inequality to the desired format without changing the problem's nature, we might interpret the instruction as asking us to leave inequalities where the constant is negative as given.
However, for the sake of the exercise, let's assume we can multiply the inequality by -1 (which would flip the inequality sign) to get:
-6x - 3y ≥ 7, though this changes the original constraint's meaning.
The second inequality is fine as is since the constant is nonnegative.
Therefore, the linear programming problem in maximized form would be:
Maximize -3x + 6y
Subject to -6x - 3y ≥ 7
3x - y ≥ -4
x ≥ 0
y ≥ 0