Problem 1: Automobile Manufacturing (17 pts) An automobile company makes 4 types of vehicles namely: regular cars (C), electric cars (E), motorbikes (M) and trucks (T). The manufacturing process involves two main steps: parts assembly and finishing touches. For the parts assembly, 2 days are required per regular car, 4 days per electric car, 1 day per motorbike and 3 days per truck. For finishing touches 2 days are required per regular/electric car, 1 per motorbike and 3 days per truck. The parts assembly and finishing touches steps should not exceed 60% and 40% of the available production time, respectively. The profit for manufacturing a regular car, an electric car, a motorbike and a truck are 10,000$, 12,000$, 5000$ and 15,000$, respectively. To limit the production of motorbikes and to promote the production of electric cars, the company makes no more than 1 motorbike in every 20 working days and makes at least 1 electric car in every 20 working days. This company would like to know how many vehicles of each type should produce in order to maxin profit in 40 days. Part A) Write the mathematical formulation for this problem (7 pts) S