The Law Firm of Smith and Jones of Barrie, Ontario has 3 new civil cases and 5 lawyers available for assignments. Based upon the type of case and the qualifications of each lawyer, the managing partners have determined the profits (in $1000’s) that the law firm would make if each particular lawyer was assigned to each particular case. Their analysis produced the following profits: Profits (1000’s) Case Lawyer A B C Lui 36 53 101 Pathak 39 54 105 Owens 43 50 103 Rosen 42 54 104 Millier 45 57 101 To keep lawyers available for future cases, Smith and Jones’ policy is to assign at most 1 lawyer to each specific case. To better serve its clients, Smith and Jones’ policy is to assign each specific lawyer to at most one case at a time. Using xij’s as your decision variables, formulate a linear programming model so that Smith and Jones’s can determine which lawyers should be assigned to which cases in order to maximize the firm’s profits while adhering to its policies and the following other restrictions. (note: When creating your model, you can use Xij’s instead of xij’s if it is too time consuming for you to use subscripts.) Millier must be assigned to a case Rosen cannot be assigned to case B Owens must be assigned to case A
The Law Firm of Smith and Jones of Barrie, Ontario has 3 new civil cases and 5 lawyers available for assignments. Based upon the type of case and the qualifications of each lawyer, the managing partners have determined the profits (in $1000’s) that the law firm would make if each particular lawyer was assigned to each particular case. Their analysis produced the following profits:
Profits (1000’s)
Case
Lawyer A B C
Lui 36 53 101
Pathak 39 54 105
Owens 43 50 103
Rosen 42 54 104
Millier 45 57 101
To keep lawyers available for future cases, Smith and Jones’ policy is to assign at most 1 lawyer to each specific case. To better serve its clients, Smith and Jones’ policy is to assign each specific lawyer to at most one case at a time. Using xij’s as your decision variables, formulate a linear programming model so that Smith and Jones’s can determine which lawyers should be assigned to which cases in order to maximize the firm’s profits while adhering to its policies and the following other restrictions. (note: When creating your model, you can use Xij’s instead of xij’s if it is too time consuming for you to use subscripts.)
- Millier must be assigned to a case
- Rosen cannot be assigned to case B
- Owens must be assigned to case A
Step by step
Solved in 3 steps with 1 images
