4. A furniture manufacturer produces wooden tables and chair. Unit profit for table is $ 6 and unit profit for chair is $8. Assuming the only to resources the company uses to produce tables and chairs are wood ( in term of board meters) and labor in term of (hours). It takes 3 board meters and 5 labor hours to make one table, while it takes two board meter and 10 labor hours to make one chair. There are 30 board meters of wood available and 110 hours of labor available. The company wishes to sell all of its tables and chairs in sets of one and four chairs each set. The company also wishes to allocate its limited resources to maximize profits.

A. Formulate the mathematical model for this problem.

B. Plot the feasible region and number the lines according to the constraints equation each one respects.

C. List the CPF solutions and their adjacent CPF solutions.

D. Calculate the profit amount for each feasible solution

E. Determine the optimal integer number of tables and chairs the manufacturer produce and sell to maximize its profits given its limited amount of resources.