6. Stickley Furniture is a manufacturer of fine hand-crafted furniture. During the next production period, management is considering producing dining room tables, dining room chairs, and/or bookcases. The time required for each item to go through the two stages of production (assembly and finishing), the amount of wood required (fine cherry wood), and the corresponding unit profits are given in the following table, along with the amount of each resource available in the upcoming production period. Tables Chairs Bookcases Available Assembly (minutes) 80 40 50 8100 Finishing (minutes) 30 20 30 4500 Wood (pounds) 80 10 50 9000 Unit Profit $360 $125 $300 After formulating a linear programming model to determine the production levels that would maximize profit and solving the model, the below sensitivity report is generated. Decision Variable Cells Final Cell Name Value Reduced Cost Objective Allowable Allowable Coefficient Increase Decrease $C$9 Production Tables 20 0 360 120 $D$9 Production Chairs $E$9 Production Bookcases 0 130 -88.33 0 125 300 88.33 60 60 1E+100 75 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$4 Assembly 8100 2 8100 900 600 $F$5 Finishing 4500 $F$6 Wood 8100 6.67 0 4500 360 1462.5 9000 1E+100 900 a) Suppose the profit per table increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit? b) Suppose the profit per chair increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit?