Multiple Choice

Question

Graph the system of constraints and find the value of x and y that maximize the objective function.
* ≥ 0
y ≥0
Constraints us!
§*+2
52 y+ x
Objective Function: C = 1x - 3y
(1 point)
• (0, 0)
• (2, 3)
• (5, 0)
• (0, 3)

Answer 1

To graph the system of constraints, we need to plot the lines representing the equations and shade the feasible region.

The first constraint is y ≥ 0, which is a horizontal line passing through the y-axis at y = 0. We shade the region above this line.

The second constraint is 52y + x ≤ 2, which can be rewritten as x ≤ -52y + 2. To graph this line, we plot two points and draw a line through them. Let's choose y = 0 and y = 1 as our points:

If y = 0, x = -52(0) + 2 = 2, so the point (2, 0) is on the line.
If y = 1, x = -52(1) + 2 = -50, so the point (-50, 1) is on the line.

We draw a line passing through these two points and shade the region below this line.

Now, we need to find the intersection of these two shaded regions, which will be our feasible region.

Looking at the graph, the feasible region consists of the points (0, 0), (2, 0), and (0, 3).

To find the value of x and y that maximize the objective function, we can substitute the coordinates of each point into the objective function and see which one gives the highest value of C.

For (0, 0):
C = 1(0) - 3(0) = 0

For (2, 0):
C = 1(2) - 3(0) = 2

For (0, 3):
C = 1(0) - 3(3) = -9

Therefore, the pair of values that maximize the objective function is (2, 0).

Answer: (2, 0)