Solve the following Linear Programming Problem via the Simplex Method: A city council is working with a hotel developer to build several hotels along its beach-front. The developer has three prototypes: a convention-style hotel with 500 rooms costing $100 million, a vacation-style hotel with 200 rooms costing $20 million, and a small hotel with 50 rooms costing $4 million. The city council wants a total capacity of at least 3,000 rooms and has three other restrictions:
• at most three convention-style hotels;
• at most twice as many small hotels as vacation-style; and
• at least a fifth as many convention-style hotels as vacation-style and small combined. How many hotels of each type should the council request in order to minimize cost? Clearly state the LPP; solve it via the Simplex Algorithm, and answer the question asked.