Use the graphical solution and/or Algebra (NOT EXCEL) to answer guestions B-12: Question 8: Let be the profit per unit of Product 1. Currently, = 30. Assume that the profit from one unit of Product 2 is fixed at its current value of $20. Determine the lower and upper limits for so that the current optimal solution remains optimal. Question 9: Assume that it is possible to increase the processing time for machine 1 from the current level of 80 hours a week to 100 hours a week. Use the graph in Figure 2 (below) to determine the optimal solution: which of the points A-G represents the optimal mix? What is the optimal value of x and y? [ What is the optimal objective value? r=diesdy [\\ ity Expansion Page 2 OIM 310 HW3 Question 10: How much will you be willing to pay to increase the capacity of machine 1 from 80 hours a week to 100 hours a week? Explain. Question 11: Consider the criginal formulation of the problem as you determined in question #1: One of the managers examined your LP model and noted that you did not take into account the requirement to run a quality assurance process for product 1 and 2. She told you that it takes 10 minutes to complete the quality assurance of a product (regardiess if itis product 1 or 2) and that there are 10 hours a week available for performing the quality assurance. Would this new constraint change the optimal product mix that you determined in gquestion 5 (and which you verified in question 6)? If yes, how would the optimal solution change? If not, explain why the new constraint does not change the optimal product mix. Question 12 Consider the criginal formulation of the problem as you determined in question #1: One of the managers examined your LP model and noted that you did not take into account the requirement that a total of at least 60 products will be produced each week. Would this new constraint change the optimal product mix that you determined in question 5 (and which you verified in question 6)7 If yes, how would the optimal solution change? If not, explain why the new constraint does not change the optimal product mix. . . . AutoSave ON n 8 7 . C 6 0 ... Pedolzky_HW3 - Saved Home Insert Draw Design Layout References > > Tell me Comments Calibri (Bo... * 12 " A A Aav Ap Paste BIUvab x x A DA Paragraph Styles Dictate Sensiti Homework #3 due 3/8/2024 Question 1: Objective function to max profit is Z=30x + 20y Subject to: 2x + 1y Add the Quality Assurance IS Revesed LP problem formulation 2- 307 / 204 machine I 2 2 1 3 4