Consider the following linear program, which maximizes profit for two products-pen (P) and notebook (N). You are producing these two items, pen and notebook. Your manufacturing environment has three type of resources: labor, paint and quality inspection hours. Assume that, the linear programming model represents your profit maximation problem. Besides, you are given the Excel answer and sensitivity reports below. Answer the following questions by analyzing the reports MAX - 100P+150N St. 2.4P+3.2N 600 Labor hours) 1.2 0.8N 300 Paint (hours 0.32PUNS 100 alty inspection (hours) P.NO Objective Cell (Max) Cell Name $B$9 Objective Profit: Original Value Final Value 0 25892.85714 Name Variable Cells Cell $B$7 Pen: $B$8 Notebook: Original Value 0 0 Final Value Integer 178.5714286 Contin 53.57142857 Contin Constraints Cell Name $F$11 Labor' thr/unit) LHS SF512 Paint (he/unit) LHS SF513 Quality Inspection thr/unit LHS Cell Value Formula Status Slack 600.00 $F$11-SH$11 Binding o 257 14 SF$12SH$12 Not Binding 42.85714286 100.00 SF$135H$13 Binding 0 Variable Cells Name Cell $857 Pen: $B$8 Notebook: Final Value 178.5714286 53.57142857 Reduced Cost 0 0 Objective Coefficient 100 150 Allowable Allowable Increase Decrease 125 40 100 16.66666667 Constraints Cell Name $F$11 Labor (hr/unit) LHS $#$12 Paint (In/unit) LHS $F$13 Quality Inspection (h/unit) LHS Final Shadow Value Price 600 35.71428571 257.1428571 100 44.64285714 Constraint Allowable Allowable R.H. Side Increase Decrease 600 54.54545455 200 300 15:30 42.85714286 100 50 20 State the optimal number of pen and notebook production, and optimal profit. If the company wants to increase the available hours for one of their constraints (labor, paint, or quality inspection, which one they should choose? Why? Support your answer by the relevant information in the report, State the optimality range for profit of the pen. Suppose we reduce the available capacity for labor hours by 50 hours. What can be said about the objective? Compute the new objective by using report information Suppose we increase the profit of the pen by ss. What can be said about the objective? Compute the new objective by using report information