Question

An electronics company has a contract to deliver 21,475 radios within the next four weeks. The clientis willing to pay $20 for each radio delivered by the end of the first week, $18 for those delivered by theend of the second week, $16 by the end of the third week, and $14 by the end of the fourth week. Sinceeach worker can assemble only 50 radios per week, the company cannot meet the order with its presentlabor force of 40; hence it must hire and train temporary help. Any of the experienced workers can betaken 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.

Required:
Formulate this as an LP problem (not necessarily in the standard form).

Answer 1

Step-by-step explanation:

See attached a detailed annotation of the LP formulation

let is describe the problem bellow.

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 week 1

$18 for each radio delivered by the end of week 2

$16 for each radio delivered by the end of week 3

$14 for each radio delivered by the end of week 4

Each worker can assemble 50 radios/wk.

Size of present workforce = 40.

Any experienced worker 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.

Weekly wages for experienced workers: $200

Weekly wages for trainees: $100

Production costs, excluding wages: $5/radio.