Linear Programming Quiz 5
 In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.
True
 Does the following linear programming problem exhibit infeasibility, unboundedness, alternate optimal solutions or solvable with one solution?
Max 3X + 3Y
s.t. 1X + 2Y > 16
1X + 1Y > 10
5X + 3Y > 45
X , Y > 0
Unboundedness
 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 both types of pen is $1000 per lot.
Which constraints are binding?
Fliptop Model 
Tiptop Model 
Available production hours 

Ink Assembly 
3 
4 
36 
Molding Time 
5 
4 
40 
Plastic 
5 
2 
30 
Ink Assembly and Molding Time
 Quentin Magic Brown manufactures sports shoes and wants to maximize the company's profits. The company makes two types of sport shoes, Airwalkers and Bouncy Basketball shoes. The company earns $10 profit on each pair of Airwalkers and $18 profit on each pair of Bouncy Basketball shoes. The manufacturing process includes cutting the materials on a machine and having workers assemble the pieces. Each pair of Airwalkers requires 3 minutes of cutting time and the Bouncy Basketball shoes require 2 minutes. The machines that cut the material can run at most 1200 minutes a week. Each worker takes 7 hours to assemble a pair of Airwalkers and 8 hours to assemble a pair of Bouncy Basketball shoes; the maximum number of hours available is 3500 per week. Determine the maximum profit for this problem?
$7875
 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?
The solution values for all the decision variables will remain the same
 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.
13,000.00
 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 binding?
Print, Fold, Print B and Print C
 Using the output below, how much is each additional unit of skilled labor worth?
Variable Cells 
Final 
Reduced 
Objective 
Allowable 
Allowable 

Cell 
Name 
Value 
Cost 
Coefficient 
Increase 
Decrease 

$B$18 
SemiAuto 
74 
0 
800 
628.5714 
432.4786 

$C$18 
Robotic 
23 
0 
1000 
1666.6667 
440 

$D$18 
Manual 
0 
320.253 
500 
320.2531 
1E+30 

Constraints 
Final 
Shadow 
Constraint 
Allowable 
Allowable 

Cell 
Name 
Value 
Price 
R.H. Side 
Increase 
Decrease 

$B$24 
Skilled labor 
4500 
5.57 
4500 
3605.2631 
1800 

$B$25 
Unskilled labor 
9000 
6.33 
9000 
3805.5556 
5850 

$B$26 
Assembly line 
1566.46 
0 
2000 
1E+30 
433.5443 
$5.570
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