Glueco produces three types of glue on three different production lines. The company has currently 15 workers in total. Workers are paid $500 per week on production line 1, $600 per week on production line 2, and $700 on production line 3. A week of production costs $1,000 to set up production line 1, $2,000 to set up production line 2, and $3,000 to set up production line 3. During a week on a production line, each worker produces the number of units of glue shown in the table below. Each week, at least 220 units of glue 1, at least 350 units of glue 2. For production to be economically feasible, at least 400 units of glue 3 must be produced. Formulate an IP to minimize the total cost of meeting weekly demands. Finally, the company can either choose to run production line 2 or 3, not both during a week.
Formulate and find the optimal solution for this problem.