Maximizing Returns and Decision Variables

This tutorial introduces linear integer programming models using binary or 0-1 variables, focusing on decision-making in yes or no situations. It covers project selection models, where binary variables indicate project selection, and fixed cost problems, where binary variables determine machine usage. The tutorial demonstrates how to maximize returns and minimize costs using these models, with examples of constraints and objective functions. The video concludes with a preview of the next tutorial on relational constraints using binary variables.

What is the primary use of binary variables in decision-making?

• To determine project duration

• To calculate project costs

• To indicate a yes or no decision

• To represent continuous variables

How is the decision variable defined for project selection?

• X1 = 0 if project 1 is selected

• X1 = 1 if project 1 is not selected

• X1 = 0 if project 1 is selected

• X1 = 1 if project 1 is selected

What is the objective when formulating the function for project selection?

• Minimize costs

• Minimize project risks

• Maximize returns

• Equalize project durations

Which of the following represents the objective function for maximizing returns?

• X1 ≤ 400, X2 ≤ 550, X3 ≤ 600

• 58X1 + 44X2 + 26X3 + 23X4

• 217X1 + 125X2 + 88X3 + 109X4

• X1 + X2 + X3 + X4

What constraint is applied to project outlays?

• They must equal available funds

• They are not constrained by available funds

• They must be greater than available funds

• They must be less than or equal to available funds

Which software can be used to solve the linear integer programming model?

• MATLAB

• Python

• LINDO or Excel Solver

• R

What is the optimal solution for project selection to maximize returns?

• X1 = 0, X2 = 1, X3 = 0, X4 = 1

• X1 = 1, X2 = 0, X3 = 1, X4 = 1

• X1 = 1, X2 = 1, X3 = 0, X4 = 0

• X1 = 0, X2 = 0, X3 = 1, X4 = 1

What is the main objective in a fixed cost problem?

• Maximize production

• Minimize total costs

• Equalize machine usage

• Maximize machine capacity

What type of decision variables are needed for fixed cost problems?

• Only binary variables

• Only continuous variables

• Both binary and continuous variables

• No decision variables are needed

How is the decision variable defined for machine usage?

• Yi = 0 if machine i is not used

• Yi = 0 if machine i is used

• Yi = 1 if machine i is not used

• Yi = 1 if machine i is used