Linear Programming and Optimization Quiz

What is the primary goal when working with linear programming problems?

• To find the feasible region and optimize the objective function

• To find the intersection of all lines

• To solve quadratic equations

• To graph linear equations

In the example of minimizing Z = 2x + 3y, what is the first step?

• Calculate the maximum value

• Graph the constraints to find the feasible region

• Solve for x and y

• Ignore the constraints

What method is used to find the intersection point of two lines in the example?

• Graphical method

• Trial and error

• Substitution method

• Elimination method

In the word problem, what are the two types of bikes the company produces?

• Mountain and hybrid bikes

• Road and electric bikes

• Mountain and road bikes

• Electric and hybrid bikes

What is the main objective in the word problem involving bike production?

• To maximize the number of bikes produced

• To minimize production time

• To minimize costs

• To maximize profit

What is the constraint related to the number of mountain bikes compared to road bikes?

• There should be at least twice as many mountain bikes as road bikes

• There should be fewer mountain bikes than road bikes

• There should be more road bikes than mountain bikes

• The number of mountain bikes should equal the number of road bikes

Which method is used to graph the constraints in the word problem?

• Graphical method

• Intercept method

• Matrix method

• Slope-intercept method

How is the maximum profit calculated in the word problem?

• By calculating the total production cost

• By guessing the maximum value

• By using the profit equation on the vertices of the feasible region

• By finding the average of all profits

What is the profit equation used in the word problem?

• Profit = 50x + 250y

• Profit = 200x + 100y

• Profit = 100x + 200y

• Profit = 150x + 150y

What is the maximum profit achieved in the word problem?

• $1800

• $2000

• $2400

• $3000