Linear Programming and Optimization Quiz

What is the primary goal of linear programming?

• To graph linear equations

• To find the maximum or minimum value of a function

• To find the average value of a function

• To solve quadratic equations

In the first example, what is the significance of the feasible region?

• It is the area where the objective function is zero

• It is the area outside the constraints

• It represents the area where all constraints are satisfied

• It is the area where the constraints are not satisfied

How do you determine the vertices of the feasible region in a graph?

• By drawing a circle around the region

• By finding the midpoint of the lines

• By identifying the intersection points of the constraint lines

• By calculating the slope of the lines

In the second example, why is there no maximum value?

• Because the constraints are not satisfied

• Because the region is unbounded

• Because the objective function is zero

• Because the region is bounded

What is the first step in solving a linear programming problem?

• Graphing the system of inequalities

• Writing the objective function

• Defining the variables

• Finding the coordinates of the vertices

Which of the following is NOT a step in linear programming applications?

• Defining variables

• Substituting coordinates into the function

• Writing a system of inequalities

• Finding the average of the coordinates

In the landscaping company example, what does the inequality 1x + 3y ≤ 9 represent?

• The total number of jobs per day

• The total hours available per day

• The total income per day

• The total number of crews available

What is the objective function used to maximize income in the landscaping example?

• 40x + 120y

• x - y

• x + y

• 2x + 3y

In the landscaping example, what is the maximum profit achieved?

• $240

• $360

• $600

• $480

Which combination of jobs maximizes the profit in the landscaping example?

• 9 mowing, 0 pruning

• 3 mowing, 2 pruning

• 2 mowing, 3 pruning

• 5 mowing, 4 pruning