Discuss the below:
Q: The Las Cruces Door Company (LCDC) designs three types of doors: Standard, HighSecurity, MaxSecurity. Each door requires different amounts of machine and labor time and has different profit margins:
|
Machine 1 |
Machine 2 |
Profit Margin |
|
Hours |
Manpower |
Hours |
Manypower |
|
| Standard |
3.5 |
5 |
4 |
6 |
$35 |
| HighSecurity |
6 |
8 |
5 |
7 |
$45 |
| MaxSecurity |
8 |
11 |
6 |
8 |
$65 |
Each door must go through both machine 1 and machine 2 before it can be sold. Each worker is assigned to work on only one of the doors, which means they work on both machines. In addition, management has decided not to sell more MaxSecurity doors than the combined total of Standard and HighSecurity doors sold, in order to keep demand high for Standard and HighSecurity doors. The LCDC has available to it only 120 hours per week on machine 1 and 100 hours on machine 2 before required maintenance, and 280 hours of manpower available per week.
1.) Formulate an LP to maximize LCDC's profit. Assume that LCDC can sell every door that they make (Ignore any integer restrictions)
2.) Use LINDO/LINGO (or other LP solver) to find the optimal solution and describe it briefly in "plain English".
3.) Add integer restrictions to the formulation in part (a), and solve using LINDO/LINGO (or other LP solver). Compare the new optimal solution with the one in part (b). What has been changed?