The Beaver Furniture Company manufactures and assembles chairs, tables, and bookshelves. The plant produces semifinished products that are assembled in the company's assembling facility. The (unassembled) monthly production capacity of the plant includes 3000 chairs, 1000 tables, and 580 bookshelves. The assembling facility employs 150 workers in two 8-hour shifts a day, 5 days a week. The average assembly times per chair, table, and bookshelf are 20, 40, and 15 minutes, respectively. The size of the labor force in the assembly facility fluctuates because of the annual leaves taken by the employees. Pending requests for leaves include 20 workers for May, 25 for June, and 45 for July. Sales of the three products for the months of May, June, and July are forecast by the marketing department as given in Table E.6. The production cost and selling price for the three products are in Table E.7. If a unit is not sold in the month in which it is produced, it is held over for possible sale in a later month. The storage cost is about 2% of the unit production cost. Should Beaver approve the proposed annual leaves?

Answer with problem formulation with constraints.

Solve problem via LINGO coding and find solution.