ISM 3011linear program quiz 5. All Solutions and Working.

• Does the following linear programming problem exhibit infeasibility, unboundedness, alternate optimal solutions or solvable with one solution? Selected Answer: unboundedness • Question 2 0.5 out of 0.5 points ...

• Does the following linear programming problem exhibit infeasibility, unboundedness, alternate optimal solutions or solvable with one solution? Selected Answer: unboundedness • Question 2 0.5 out of 0.5 points The point (3, 2) is feasible for the constraint 2x + 6y ≥ 30. Selected Answer: False • Question 3 0.5 out of 0.5 points Quill Manufacturing Business makes two models of marking pens. An unlabeled graph for this problem and the requirements for each lot of pens in the three manufacturing departments are given below. All three departments are necessary in the production of both types of pens. The profit for either kind of pen is $1000 per lot. An unlabeled graph for this problem is given below with a dotted line representing the objective function line. If all of the constraint inequalities in the original problem were “>” (i.e. greater than or equal), which of the following statements would be true? Selected Answer: The problem will become unbounded • Question 4 0.5 out of 0.5 points Consider the following linear programming problem. What is the optimal value of the objective function? X, Y ≥ 0 Selected Answer: The value of the objective function is 59 • Question 5 0.5 out of 0.5 points Using the output below, determine the objective function value (profit). Variable Cells $B$18SemiAuto 74 0 800 628.5714 432.4786 $C$18Robotic 23 0 1000 1666.6667 440 $D$18Manual 0 -320.253 500 320.2531 1E+30 Constraints $B$24Skilled labor 4500 5.57 4500 3605.2631 1800 $B$25Unskilled labor 9000 6.33 9000 3805.5556 5850 $B$26Assembly line 1566.46 0 2000 1E+30 433.5443 Selected Answer: 82,200 • Question 6 0.5 out of 0.5 points Quality Bike Maps has produced four map designs for the local area. A limited amount of time (in minutes) is allocated to the printing, cutting and folding of each map. Additionally, at least one thousand of map designs A, B, and C must be printed. The profit per map is $1 for A and B and $2 for C and D. Use the Report below and assume the current objective function value is $10,166.67, to determine the new objective function value if the profit for Map D increases by $1. Variable Cells Final Reduced Objective Allowable Allowable Constraints • Question 7 0.5 out of 0.5 points Using the output below, if the RHS of the Unskilled Labor constraint increases by 100, by how much will the objective function value increase? $633 • Question 8 0.5 out of 0.5 points Quality Bike Maps has produced four map designs for the local area. A limited amount of time (in minutes) is allocated to the printing, cutting and folding of each map. Additionally, at least one thousand of map designs A, B, and C must be printed. The profit per map is $1 for A and B and $2 for C and D. Using the Report below, which constraint(s) are NOT binding? Variable Cells Friday, December 2, 2016 11:53:24 AM EST • 0.5 out of 0.5 points Which of the following statements is correct regarding the linear programming model Selected Answer: Constraint 3 is a redundant constraint • Question 2 0 out of 0.5 points Quill Manufacturing Business makes two models of marking pens. An unlabeled graph for this problem and the requirements for each lot of pens in the three manufacturing departments are given below. All three departments are necessary in the production of both types of pens. The profit for either kind of pen is $1000 per lot. An unlabeled graph for this problem is given below with a dotted line representing the objective function line. What is the optimal production quantity for the Tiptop model? Selected Answer: 4 lots • Question 3 0.5 out of 0.5 points Quill Manufacturing Business makes two models of marking pens. An unlabeled graph for this problem and the requirements for each lot of pens in the three manufacturing departments are given below. All three departments are necessary in the production of both types of pens. The profit for either kind of pen is $1000 per lot. An unlabeled graph for this problem is given below with a dotted line representing the objective function line. If all of the constraint inequalities in the original problem were “>” (i.e. greater than or equal), which of the following statements would be true? Selected Answer: The problem will become unbounded • Question 4 0.5 out of 0.5 points A section of output from Excel Solver is shown below. Product A 150 0 100 20 40 Product B 100 0 300 120 60 What will happen to the solution if the objective function coefficient for Product A increases by 30? Selected Answer: The problem will need to be resolved to find the new optimal solution and shadow prices. • Question 5 0.5 out of 0.5 points A linear program has been solved and sensitivity analysis has been performed. The ranges for the objective function coefficients have been found. For the profit on X, the upper bound is 80, the lower bound is 60, and the current value is 75. Which of the following must be true if the profit on this variable is lowered to 70 and the optimal solution is found? Selected Answer: The solution values for all the decision variables will remain the same • Question 6 0 out of 0.5 points As long as the slope of the objective function stays between the slopes of the binding constraints Selected Answer: the value of the objective function won’t change. • Question 7 0.5 out of 0.5 points Quality Bike Maps has produced four map designs for the local area. A limited amount of time (in minutes) is allocated to the printing, cutting and folding of each map. Additionally, at least one thousand of map designs A, B, and C must be printed. The profit per map is $1 for A and B and $2 for C and D. Using the Report below, if the RHS of the Print constraint increased by100, by how much will the objective function value change? Variable Cells The objective function value will increase by 50 • Question 8 0.5 out of 0.5 points Using the output below, if the RHS of the Unskilled Labor constraint increases by 100, by how much will the objective function value increase? Variable Cells Selected Answer: $633 Friday, Decemb• 0 out of 0.5 points Quill Manufacturing Business makes two models of marking pens. An unlabeled graph for this problem and the requirements for each lot of pens in the three manufacturing departments are given below. All three departments are necessary in the production of both types of pens. The profit for either kind of pen is $1000 per lot. An unlabeled graph for this problem is given below with a dotted line representing the objective function line. If all of the constraint inequalities in the original problem were “>” (i.e. greater than or equal), which of the following statements would be true? Selected Answer: There will be multiple optimal solutions • Question 2 0.5 out of 0.5 points Consider the following linear programming problem. What are the binding constraint(s)? X, Y ≥ 0 Selected Answer: B & C • Question 3 0 out of 0.5 points Does the following linear programming problem exhibit infeasibility, unboundedness, alternate optimal solutions or solvable with one solution? X , Y > 0 Selected Answer: solvable with one solution • Question 4 0.5 out of 0.5 points Quality Bike Maps has produced four map designs for the local area. A limited amount of time (in minutes) is allocated to the printing, cutting and folding of each map. Additionally, at least one thousand of map designs A, B, and C must be printed. The profit per map is $1 for A and B and $2 for C and D. Using the Report below, if the RHS of the Print constraint increased by100, by how much will the objective function value change? Variable Cells