Answer:
To determine whether the given linear program can be solved graphically, we need to check if the feasible region (the region where all constraints are satisfied) is bounded or unbounded.
The constraint in the linear program is 3x - 4y ≤ 0. If we rearrange this constraint to isolate y, we have:
y ≥ (3/4)x
This constraint represents a half-plane where y is greater than or equal to (3/4)x. Since the inequality does not have a strict inequality (≤ instead of <), the feasible region includes the boundary line y = (3/4)x.
Now, let's consider the objective function z = 60x + 80y. Since the objective function is a linear function, the optimal solution, if it exists, will occur at one of the extreme points of the feasible region.
However, in this case, the feasible region extends infinitely along the line y = (3/4)x. Therefore, the feasible region is unbounded, and we cannot find an optimal solution graphically.
Therefore, the statement is false. The given linear program cannot be solved graphically because the feasible region is unbounded.
