Linear Programming
Budget: $30 – $250 USD
An electronics company has a contract to deliver 21,475 radios within the next four weeks. The client is willing to pay $20 for each radio delivered by the end of the first week, $18 for those delivered by the end of the second week, $16 by the end of the third week, and $14 by the end of the fourth week. Since each worker can assemble only 50 radios per week, the company cannot meet the order with its present labor force of 40; hence it must hire and train temporary help. Any of the experienced workers can be taken off the assembly line to instruct a class of three trainees; after one week of instruction, each of the trainees can either proceed to the assembly line or instruct additional new classes.
At present, the company has no other contracts; hence some workers may become idle once the delivery is completed. All of them, whether permanent or temporary, must be kept on the payroll 'til the end of the fourth week. The weekly wages of a worker, whether assembling, instructing, or being idle, are $200; the weekly wages of a trainee are $100. The production costs, excluding the worker's wages, are $5 per radio. The company's aim is to maximize the total net profit. Formulate this as an LP problem (not necessarily in the standard form)
1. Model the problem as an LP
2. Solve the LP using the software package of your choice, and provide an optimal solution and the corresponding optimal objective function value.
3. Write a brief report commenting on the nature of the solution. This report should be accompanied by the solution to the LP, the solution to the dual, and the range values for the right-hand sides and the objective coefficients. In particular, you should comment on the robustness of the solution indicating the most sensitive elements of the model
a. discussion of the sensitivity report with a couple of scenarios explored. Each scenario should be accompanied by its own sensitivity report.
At present, the company has no other contracts; hence some workers may become idle once the delivery is completed. All of them, whether permanent or temporary, must be kept on the payroll 'til the end of the fourth week. The weekly wages of a worker, whether assembling, instructing, or being idle, are $200; the weekly wages of a trainee are $100. The production costs, excluding the worker's wages, are $5 per radio. The company's aim is to maximize the total net profit. Formulate this as an LP problem (not necessarily in the standard form)
1. Model the problem as an LP
2. Solve the LP using the software package of your choice, and provide an optimal solution and the corresponding optimal objective function value.
3. Write a brief report commenting on the nature of the solution. This report should be accompanied by the solution to the LP, the solution to the dual, and the range values for the right-hand sides and the objective coefficients. In particular, you should comment on the robustness of the solution indicating the most sensitive elements of the model
a. discussion of the sensitivity report with a couple of scenarios explored. Each scenario should be accompanied by its own sensitivity report.