Joyce Lumber Company Joyce Lumber Company produces tables and chairs. The production process for each is similar in that both require a certain number of labor hours in the carpentry department and a certain number of hours in the painting department. Each table takes three hours of carpentry work and two hours of painting work. Each chair requires four hours of carpentry and one 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 the company to make no more than 450 new chairs this month because of an overabundance of available chairs. However, because the existing inventory of tables is low, the marketing, department wants the company to make at least 100 tables this month. Each table sold makes a profit contribution of $7 and each chair sold makes a profit of $5. Joyce Lumber's problem to determine the best possible combination of tables and chairs to manufacture this month in order to attain the maximum profit. The firm would like to solve this as a linear programming problem. Use the information below to answer the following questions. Joyce Lumber Co. a) What is the optimal production solution to this problem? What is the total profit? b) What are the allowable numbers of chairs and tables that can be produced before the optimal solution changes? c) What is the impact on profits of a decrease in painting time of 100 hours? Does the optimal solution change? d) What is the impact on profits of an increase in carpentry time of 200 hours? Does the optimal solution change? e) Will the optimal solution change if the market price is able to increase and the profit per chair increases $4