only answer number 8. ive attached previous questions for reference

8. Below are both the Answer and Sensitivity reports for the same Bike problem. Use them to answer the following questions. Optimal Objective Value $71,250 Variable XI X2 Value 50 0 Reduced Cost 0 -60 0 0 75 X4 140 Slack/Surplus Constraint 11 - Carbon Alloy Availability, Ibs #2 - Manufacturing Time, hrs #3 - Combined Production Total #4 - Min # of Aerodyne Max 0 0 Dual Value 50 5 0 15 0 -75 Variable X1 Allowable Increase 75 60 50 8.33 Ob Coefficient 400 300 370 300 X2 Allowable Decrease 1E+30 16.30 10 34.09 X3 X4 Constraint 11 - Carbon Alloy Avail, Ibs #2 - Manufacturing Time, hrs 13. Combined Production #4 - Min of Aerodyne Max RHS Value 1250 2500 200 50 Allowable Increase 25 150 15 21.4 Allowable Decrease 37.5 50 1E+30 50 (a) What is the Range of Optimality for the objective coefficient for the Men's Road Ranger? (b) The expected profit for the Men's Road Ranger has increased by $80/bike because of supplier cost decreases. Should you produce any Road Rangers? Yes or No (c) What is the Range of Feasibility for the Available Carbon Alloy Limitation? (d) The available Manufacturing Time has decreased to 1230 hours because of machine repairs. What is your new profit? $ 7. The Answer Report for the above problem is provided below. Use it and your LP formulation to answer the following: Optimal Objective Value $71,250 Value Reduced Cost Variable X1 X2 50 0 -60 X3 0 25 140 0 X4 0 Constraint #1 - Carbon Alloy Availability, Ibs #2 - Manufacturing Time, hrs #3 - Combined Production Total #4 - Min # of Aerodyne Max Slack/Surplus 0 0 Dual Value 50 5 15 0 0 -75 (a) Which constraint has any Slack/Surplus? (b) Slack or Surplus? (c) How much? (d) Which constraints are binding? (e) If we require one Men's Road Ranger be made, what is the new profit? $ 6. The Answer Report for the above problem is provided below: Optimal Objective Value $71,250 Reduced Cost 0 Variable X1 X2 X3 X4 Value 50 0 25 140 -60 0 0 Constraint #1 - Carbon Alloy Availability, Ibs #2 - Manufacturing Time, hrs #3 - Combined Production Total #4 - Min # of Aerodyne Max Slack/Surplus 0 0 Dual Value 50 5 0 -75 15 0 For the next production period, how many of each cycle should be made? (a) # of Men's Aerodyne bikes = (b) # of Men's Road Ranger bikes = (c) # of Women's Lady Aerodyne (d) # of Featherweight Flyers What is the optimal expected profit? $ 5. Cannon Cycles produces a number of aerodynamic and long distance road bikes for cycling enthusiasts which are sold on-line. For the upcoming production period, four specific models will be produced because of increased demand after the recent Tour de France in August. They are: a Men's Aerodyne Max; a Men's Road Ranger; a Women's Lady Aerodyne; and a Featherweight model for mountain racing. The four models all use a special carbon alloy. The amount of alloy required for each model is summarized in the table below along with the anticipated profit per bike and the manufacturing time required. There are 1250 lbs of carbon alloy and 2500 hours of manufacturing time are available during the next production period. X-Aerodyne Max X-Road Ranger X-Lady Aerodyne X-Featherweight Flyer UnitPro S/be 400 300 375 300 Carbon Alloy. Ibs 8 6 6 5 Manufacturing Time, hers 15 12 14 10 There must be a combined production of at least 200 bikes. Lastly, at least 50 of the Men's Aerodyne Max Bikes must be produced. In the space below, write the objective function and ALL constraints for this problem using the above decision variables as defined. (eg, X1 = # of Men's Aerodyne Max bikes; X2 = # of Road Ranger bikes, etc.)