Consider the following linear program, which maximizes profit for two products-pen (P) and notebook (N). You are producing those 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 maximization problem. Besides, you are given the Excel answer and sensitivity reports below. Answer the following questions by analyzing the reports. MAXZ=100p+150N s.t. 2.4P+3.2NS600 Labor (hours) 1.2P+0.8N300 Paint (hours) 0.32P+0.8N100 Quality inspection (hours) P,N0 Answer Report: Sensitivity Report: State the optimal number of pen and notebook producton, 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 shouid 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 avalable 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 $5. What can be soid about the objective? Compute the new objective by using report information