In a linear programming problem,the inequalities,X + 2Y ≤ 12 and 3X + 4Y  28,hold as binding constraints.The problem's optimal solution would be:
A)X = 4,and Y = -4.
B)X = 4,and Y = 8.
C)X = 4,and Y = 4.
D)X = 8,and Y = 4.
E)X = Y = 8.

Question

Quizplus · Accepted Answer

Since X + 2Y = 12 is a binding constraint, we know that the optimal solution must lie on this line. Similarly, since 3X + 4Y = 28 is a binding constraint, the optimal solution must also lie on or above this line.

If we plot both lines on a graph, we can see that they intersect at (4, 4). This point is within the feasible region, which is given by the shaded area in the graph below:

```
    |
12  |    A
    |   / \
    |  /   \
    | /     \
 8  |/       \
    *--------*--------*--------*--------*--------*
            4        6        8        10       12
                    X-axis
```

Therefore, the optimal solution is X = 4 and Y = 4.

In a Linear Programming Problem,the Inequalities,X + 2Y ≤ 12