hi show all steps (Linear Optimization&Modeling Homework)

8. A company has a contract to deliver 20,000 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 till the end of the fourth week. The weekly wages of a worker (assembling, instructing, or being idle) are $200 and the weekly wages of a trainee are $100. The production cost is $5 per radio. (a) Formulate an LP that maximizes the company's total net profit under the conditions described above. (b) Use an optimization solver (your favorite one or one of the software packages listed on the course syllabus) to solve the LP you formulated in (a)