Please answer the following questions in the space provided below (either write it down or type). You also need to submit the Excel file with all the work. You will not receive the full credits without the supporting analysis. You will submit two files for this assignment: a. Word document with all the answers; b. Excel file with all the work.

1. Furniture Inc. makes two products, tables and chairs, which are processed through the Assembly and Finishing departments. Each table takes 5 hours sanding time, 4 hours painting and 6 hours assembly. Each chair takes 6 hours of sanding, 2 hours painting and 2 hours assembly. This week, we have 60 hours for sanding, 24 hours for painting and 48 hours for assembly. The profit is $5 per table and $3 per chair. The company wants to determine how many tables and chairs should be manufactured this week to maximize profits?

a. Write the mathematical formulation for the above mathematical problem and turn-in the handwritten solution (neatness counts). [5 points]

b. Use excel solver to find the optimal solution and the optimal objective value. Assume you can produce a fraction of a chair and a table (write your answers in the space below). [Create your own template in Excel]. [5 points]

c. You have three resources (sanding, painting, and assembly). Which of these resources are critical and non-critical? [5 points]

d. If we work overtime, we get an additional 10 hours in the paint shop. Based on the sensitivity report, can you predict how the optimal solution and the objective function will be affected? How will they change? [5 points]

e. The additional cost of overtime in the painting department is $1 per hour. Is it profitable to run overtime? [5 points]

f. If you cannot produce a fraction of chair and a table (obviously). What is the optimal solution and the optimal objective value? [5 points]