Model 7: Electronics Company
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).