a company manufacturers a product which goes through five operations. the company has identified the information on production rates, costs and weekly capacities of the current system as provided in the table below. the material supplier of the company is able provide only $250$ kg of a specific material per week to be used $100$g for each unit of the product. the manufacturing company is in the process of achieving it satisfaction output rate for the product that can be sold at most $2,000$ units per week the price of $50$ Tl$/$unit$.$ company has made an agreement with the subcontractor that can process after $1,800$ units per week for operation $3$ with a unit of cost of $12$ tl$.$ the subcontractor will receive the items that have passed the operation $2$ process them for operation $3$ with a scrap rate of $1\%$ and then deliver the quality item to the manufacturer for the next operations $.$additionally, an overtime shift of $50$ hours per week defined for operation $4$ at the main plant $.$ overtime operation will increase the production cost by a scrap of $5\%$ is expected due to mistakes made by tired workers. formulate a mathematical model will determine the weekly production plan of this company