Question

Objects function: C = x + 2y. Constraints: x > 0, y > 0, x + y < 3. Find the minimum and maximum values of the object function subject to the given constraints.

A) Min = 1, Max = 3
B) Min = 0, Max = 3
C) Min = 2, Max = 4
D) Min = 1, Max = 5

Answer 1

C) Min = 2, Max = 4. To find the minimum and maximum values of the object function C = x + 2y subject to the given constraints, graph the constraints and examine the feasible region. The minimum value of C is 1 and the maximum value of C is 4.

Step-by-step explanation:

To find the minimum and maximum values of the object function C = x + 2y subject to the given constraints, we need to examine the feasible region determined by the constraints. First, let's graph the constraints:

• x > 0 is a vertical line to the right of the y-axis.
• y > 0 is a horizontal line above the x-axis.
• x + y < 3 is a line with a negative slope passing through (3, 0) and (0, 3).

The feasible region is the area in the first quadrant bounded by these lines. The object function C = x + 2y will have its minimum value at the vertex of the feasible region with the lowest value of C, and its maximum value at the vertex with the highest value of C.

After graphing and examining the feasible region, we can determine that the minimum value of C is 1 and the maximum value of C is 4. Therefore, the correct answer is C) Min = 1, Max = 4.