Steel Door Co. produces two types of steel doors, Door 1 and Door 2, in its

three work shops: Shop 1 produces plastic parts, and Shop 2 produces wood parts. Shop 3 is dedicated to producing steelframes and assembly. Door 1 requires processes in Shop 1 and then Shop 3. Door 2, on the other hand, requires processes in Shop 2 and then Shop 3. Hence, both products compete for the production time available in Shop 3. Specifically, one batch of Door 1 needs 4 hours of processing in Shop 1 and 3 hours in Shop 3. One batch of Door 2 requires 2 hours of processing in Shop 2 and 2 hours of processing in Shop 3. Total production time available in Shops 1, 2, and 3 are 4, 12, and 18 hours per week, respectively. One batch of Door 1 earns 3000 TL profit (excess revenue over costs) whereas Door 2 is more profitable, 5000 TL per batch. The company has no demand considerations, it can sell all the doors it produces. Steel Door Co. wants to maximize its profits. How many batches of each product would you produce per week? (Note that fractional values are valid: E.g., 2.5 batches per week means produce 5 batches every 2 weeks. In other words, we are interested in the rate of production, we are not planning for just one week).

1. (2 points) What is the performance measure? Can you formulate it as an objective function by defining appropriate decision variables?
2. (6 points) What are the constraints? Formulate them mathematically.
3. (2 points) How many feasible solutions are there?
4. (5 points)Which feasible solutionis the best in termsof the objective function you formulate in part (a)?
5. (5 points) If the available production time in Shop 1 is 5 hours per week (in- stead of 4), how will your answer change?