A furniture store manufactures 2 products; tables (X) and chairs (Y): the production process for each require a certain number of labor hours in the carpentry department and a certain number of labor hours in the painting department. Each table takes 3 hours of carpentry work and 2 hours of painting work. Each chair requires 4 hours of carpentry and 1 hour of painting. During the current month, 2,400 hours of carpentry time and 1,000 hours of painting time are available. The marketing department wants no more than 450 new chairs this month because of existing large inventory of chairs. However, the marketing department wants to make at least 100 tables this month because of low inventory of tables. Each table brings in $7 profit and each chair yields $5 profit. The manger wants to determine the best possible combinations of tables (X) and chairs (Y) to manufacture this month in order to earn maximum profit. Formulate this situation as a LP problem and find an optimum solution (i.e., the best combination of X and Y) i) by trial and error method, and ii) graphically. Do not forget to identify the feasible region when you draw these constraints on a graph.