Question 1: Using a graphing calculator, find and select all the vertices for the feasible region.
To find the vertices of the feasible region, we need to graph the inequalities and determine where they intersect. Using a graphing calculator or software, we can plot the two inequality lines and shade the area that satisfies both conditions.
The graph shows that the feasible region is a triangle formed by three lines:
1. y ≥ -x + 3 (represented by the line in the first quadrant with slope -1 and y-intercept 3).
2. y ≤ 1/3x + 1 (represented by the line with slope 1/3 and y-intercept 1).
3. x ≥ 0 and y ≥ 0 (representing the positive x and y axes).
The vertices of the feasible region are the intersections of these lines.
From the given options, the vertices of the feasible region are:
(0, 3), (3, 0), and (1.5, 1.5)
Question 2: Which vertex of the feasible region from above would maximize the objective function? (Make sure to show all necessary steps to support your answer.)
To determine which vertex of the feasible region maximizes the objective function C = 5x - 4y, we need to evaluate the objective function at each vertex and compare the values.
1. C(0, 3) = 5(0) - 4(3) = -12
2. C(3, 0) = 5(3) - 4(0) = 15
3. C(1.5, 1.5) = 5(1.5) - 4(1.5) = 1.5
Therefore, the vertex (3, 0) maximizes the objective function.
Question 3: What is the maximum value for C?
The maximum value for C occurs at the vertex (3, 0), which is 15. Therefore, the maximum value for C is 15.
Use the following constraints and objective function to answer the next 3 questions.
x >/ 0
y >/ 0
-x + 3 >/ y
y </ 1/3x + 1
Objective function: C=5x−4y
Question 1: Using a graphing calculator, find and select all the vertices for the feasible region.
Responses
(0,3)
(3,0)
(0,0)
(1.5,1.5)
(-3,0)
(1,0)
(0,1)
Question 2 Which vertex of the feasible region from above would maximize the objective function? (Make sure to show all necessary steps to support your answer.)
Question 3 What is the maximum value for C?
1 answer