Question

Part I: Multiple Choice 1. The Bamboo Furniture Company manufactures two main products, chairs and recreational tables, for use in summer homes and outdoor porched-in areas. The firm has two main resources: its carpenters (labor) and a supply of Bamboo for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good quality Bamboo. Each chair that Bamboo Furniture produces requires 4 hours of labor and 10 feet of Bamboo; each recreational table takes 6 hours of labor and 35 feet of Bamboo. Completed chairs will yield a profit of $9 each, and tables will yield a profit of $20 each. How many tables and chairs should Bamboo Furniture produce to obtain the largest possible profit? What if the demand for the style of outdoor chairs increases this season so that the price can rise and profits increase from $9 to $11 each, will the optimal solution (production mix) change? If, as a result of a reorganization of the production assembly floor layout, the carpenter labor requirement for each table is reduced from 6 to 5 hours, will the optimal solution change as a result, that is, will the production mix of tables and chairs change as a result? Show all work

Answer 1

1) x be number of chairs y be tables Maximise 20y + 9x subject to 35y + 10x lessthanequalto 3500 6y + 4x lessthanequalto 1200 Maximum profit = 2862.5 x = 262.5 y = 25 b) change from 9 to 11 production min change doesn't occure. C) from 6 to 5 production change occurs x = 272.22 y = 22.22