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 non slippery; whereas wall tiles are made with 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. Each batch of wall tiles needs 2 hours of Machine 1 and 3 hours of Machine 2. Machine 1 has a maximum of 120 hours of production time and Machine 2, 90 hours. The machines can produce tiles in whole number of batches and in fraction of a batch. Production of floor tiles needs 2 workers and production of wall tiles needs 4 workers. Presently, the company employs 100 workers. Each batch of floor tiles earns a profit of €2,000 and wall tiles, €3,000. The company wants to satisfy the following goals:
(1) The company hires Machine 1 and wants to use it efficiently; therefore, it does not want to use fewer than 120 hours of Machine 1 time but at the same time the excess time of Machine 1 is limited to 40 hours.
(2) The company wants to achieve a profit of €120,000.
a. Formulate a goal programming model to the problem.
b. Solve the model using computer.