Linear programming, True false and Fill in the blanks

TRUE/FALSE

1. Linear programming is a model consisting of linear relationships representing a firm’s decisions given an objective and resource constraints.

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2. The objective function is a linear relationship reflecting the objective of an operation.

3. A linear programming model consists of decision variables, constraints, but no objective function.

4. A feasible solution violates at least one of the constraints.

5. In a linear programming model, the number of constraints must be less than the number of decision variables.

6. Linear programming models have an objective function to be maximized but not minimized.

7. Linear programming models exhibit linearity among all constraint relationships and the objective function.

8. The graphical approach to the solution of linear programming problems is a very efficient means of solving problems.

9. Slack variables are only associated with maximization problems.

10. Surplus variables are only associated with minimization problems.

FILL IN THE BLANK

Model Formulation

11. ____________________are mathematical symbols representing levels of activity.

12. A graphical solution is limited to solving linear programming problems with only ___ decision variables

13. The optimal solution to a linear programming model always occurs at a (an) _________ point of the feasible region.

14. Multiple optimal solutions can occur when the objective function line is __________ to a constraint line.

15. The _______________ property of linear programming models indicates that the decision variables cannot be restricted to integer values and can take on any fractional value.

PROBLEM SOLVING

16. Consider the following minimization problem.
Min z = x1 + 2×2
s.t. x1 + x2 300
2×1 + x2 400
2×1 + 5×2 750
x1, x2 0
Which constraints are binding at the optimal solution? (x1 = 250, x2 = 50)

17. Consider the following minimization problem.
Min z = 1.5×1 + 2×2
s.t. x1 + x2 300
2×1 + x2 400
2×1 + 5×2 750
x1, x2 0
What are the optimal values of x1, x2, and z?

18. Consider the following linear programming problem:
Max Z = $15x + $20y
Subject to : 8x + 5y 40
0.4x + y 4
x, y
Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?

19. Consider the following linear programming problem

MIN Z = 10×1 + 20×2
Subject to: x1 + x2 12
2×1 + 5×2 40
x2 13
x1 , x2 0
What are the values of x1 and x2 at the extreme points of the feasible region ?

20. Consider the following linear programming problem

MIN Z = 10×1 + 20×2
Subject to: x1 + x2 12
2×1 + 5×2 40
x2 13
x1 , x2 0
At the optimal solution, what is the value of surplus and slack associated with constraint 1 and constraint 3 respectively ?

21- Explain the difference between profit and contribution in an objective function. Why is it important for the decision maker to know which of these the objective function coefficients represent?

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