Reference no: EM131922041
A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table.
| Product |
Material #1 (pounds) |
Material #2 (pounds) |
Labor Hours |
| A |
3 |
2 |
4 |
| B |
1 |
4 |
2 |
| C |
5 |
0 |
3.5 |
Courtesy of Terry Klinker
Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product A sells for $101 a unit, product B sells for $67 a unit, and product C sells for $97.50 a unit. Each week there are 300 pounds of material #1; 400 pounds of material #2; and 200 hours of labor. Moreover, there is a standing order of 10 units of product C each week.
Linear Programming Formulation
Maximize: 10A + 10B + 10C
Subject to:
3A + 1B + 5C = 300 (constraint #1)
2A + 4B = 400 (constraint #2)
4A + 2B + 3.5C = 200 (constraint #3)
C = 10 (constraint #4)
All decision variables > 0
Sensitivity Report
Adjustable Cells
| Cell | Name | Final Value | Reduced Cost | Objective Coefficient | Allowable Increase | Allowable Decrease |
| $B$4 |
Optimal Values: A |
0 |
-10 |
10 |
10 |
1E+30 |
| $C$4 |
Optimal Values: B |
82.5 |
0 |
10 |
1E+30 |
4.285 |
| $D$4 |
Optimal Values: C |
10 |
0 |
10 |
7.5 |
1E+30 |
Courtesy of Terry Klinker
Constraints
| Cell | Name | Final Value | Shadow Price | Constraint R.H.S. Side | Allowable Increase | Allowable Decrease |
| $E$7 |
Constraint 1 |
132.5 |
0 |
300 |
1E+30 |
167.5 |
| $E$8 |
Constraint 2 |
330 |
0 |
400 |
1E+30 |
70 |
| $E$9 |
Constraint 3 |
200 |
5 |
200 |
35 |
165 |
| $E$10 |
Constraint 4 |
10 |
-7.5 |
10 |
47.142 |
10 |
Courtesy of Terry Klinker
1.The production manager adds an addition laborer, increasing labor hours by 40. What impact will this have on the current objective function value?
2.Suppose that the production manager has an additional 100 pounds of material 1. What impact will this have on the current optimal objective function value?
|
What source system would the him professional investigate
: If an HIM professional was assessing the integrity of the information captured in the hospital registration process.
|
|
Compute overall system reliability under plan
: A production line has three machines A, B, and C, with reliabilities of .93, .94, and .89, respectively. The machines are arranged so that if one breaks down.
|
|
Write a literary analysis over one of pieces of literature
: write a minimum of a 1,000-word literary analysis over one of pieces of literature. What will help you is using the right words when you're doing your search.
|
|
What type of report might a service organization use
: What type of report might a service organization use as a marketing tool to provide potential customers information about the internal controls related.
|
|
What impact will this have on the current objective function
: A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits.
|
|
Prepare journal entries to record the transactions
: Prepare journal entries to record the above transactions assuming Urban Faith has a December 31 year end. Be sure to prepare the appropriate closing entries.
|
|
What is the maximum profit based on your optimal solution
: What is the maximum profit based on your optimal solution (the value of the objective function)?
|
|
Biggest employment challenge at their organization
: In a study of 405 nonprofits? nationwide, 87 indicated that turnover has been the biggest employment challenge at their organization. Complete parts? (a) throug
|
|
Which operation is the bottleneck
: The drilling operation occurs separately from, and simultaneously with, the sawing and sanding operations.
|