An automobile manufacturer has five outdated plants: one each in Michigan, Ohio, and California and two in New York. Management is considering modernizing these plants to manufacture engine blocks and transmissions for a new model car. The cost to modernize each plant and the manufacturing capacity after modernization are as follows:An automobile manufacturer has ?ve outdated plants: one each in Michigan, Ohio, andCalifornia and two in New York. Management is considering modernizing these plants tomanufacture engine blocks and transmissions for a new model car. The cost to modernizeeach plant and the manufacturing capacity after modernization are as follows: Cost Engine Blocks TransmissionsPlant ($ millions) (10005) (1000s)Michigan 25 500 300New York 35 800 400New York 35 400 800Ohio 40 900 600 facturing needs and, at the same time, minimize the total cost of modernization. a. Develop a table that lists every possible option available to management. As part ofyour table, indicate the total engine block capacity and transmission capacity for eachpossible option, whether the option is feasible based on the projected needs, and thetotal modernization cost for each option. b. Based on your analysis in part (a), what recommendation would you providemanagement? c. Formulate a 0-1 integer programming model that could be used to determine the opti-mal solution to the modernization question facing management. (1. Solve the model formulated in part (c) to provide a recommendation for management.