HAK company hires new graduate student, Josh B ,but this recruitment process took 6 months after his graduation and he has a cumulative debt of 400 USD before starting his new position. His starting monthly gross salary is 5.000 USD including 25% income tax. In addition, he has several expenditures for his daily and social life organizations, such as loan payment of 1.000 USD/month for his new luxury car; 1.500 USD/month for mortgage credits; and expected monthly living cost is around 1.250 USD. Apart from these fixed expenditures, Mr. B also spending some of his budget to the sport and cultural activities. He makes payment of 100 USD every two months to his Gym Facility; 150 USD every three months to his KYK credit debt and 50 USD for cultural activities every month. He starts his initial payments at the end of first month. He has also another option to earn more money by using his savings in BCOIN platform. In this platform, people can earn 10% of their investments but they should wait 2 months. This means that for example, if you put 100 USD to this platform at the end of Month 1, you will get 110 USD at the beginning of Month 4. Moreover, another option to meet financial requirements is to get express credit loan from banks by paying 20% interest rate one time next month and you can pay back with equal payments next 3 months.

a. Develop mathematical model for budget management of Mr. B (show your constraints explicitly)

b. Find the feasible solution for budget management of Mr. B next eight months