An interior design and construction company produces two types of tiles—floor tiles and wall tiles. Floor tiles are made with slightly rough surface to make it nonslippery, whereas wall tiles are given a smooth and mirror finish. The company currently uses two machines to produce these tiles. Each batch of floor tiles needs 3 hours of Machine 1 and 2 hours of Machine 2 Machine 1 has a maximum of 120 hours of production time and Machine 2, 90 hours. Production of a batch of floor tiles needs 2 workers and a batch of wall tiles needs 4 workers. Presently, the company employs 100 workers. 

Each batch of floor tiles earn a profit of €2,000 and wall tiles, €3,000. The company wants to determine the number of batches to be produced for each type to maximize profit.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.