1. Rose Bay Boatworks will be closing their facility in two months time so that major renovations can be done. They will be closed for almost 6 months and so want to make best use of resources that they have available before they close: R88 specializes in small watercraft, including canoes, kayaks, and dinghy's. These are made using two processes. The kayaks are made from polyethylene plastic that is heated in molds, whereas the other products are made from layers of fiberglass or Kevlar that are built in layers over a mold. In all cases after the basic watercraft shape is made, it requires some further cutting and finishing as well as the installation of fittings, inspection, and packaging. RBB formulated their problem as a linear program as follows: C1 = # of small canoes C2 = # of regular canoes K1 = # of one person kayaks K2 = # of two person kayaks D = # of dinghy's 22,861 + 2.3K2 Maximize Profit - $3201 + $4102 +S42K1 + $55K2 + $25D Subject to: Kayak mold prep time 2.0K1 + 2.1K2 Kayak oven time Kevlar/fiberglass time 2.201 + 2.5C2 Cutting/finishing time 1.5C1 + 1.5C2+1.8K1 - 2.0K2 Fitting installation time 1.5C1 + 2.0C2 +2.2K1 - 2.7K2 Minimum Canoe output C1+C2 Minimum Kayak output Kl. K2 Minimum Dinghy output D Non negativity C1, C2, K1, K2, D $ 120 hours s 240 hours + 1.6D S 210 hours +0.9D S 320 hours +1.40 S 320 hours 250 250 10 20 The Sensitivity Report is given below: 6 Variable Cells Final Reduced Objective Allowable Allowable B Cell Name Value Cost Coefficient increase Decres 9 R4C2 made Small Canoe 13:4055934 0 32 4.08 12162963 10 R4C3 # made Regular Cance 65.8021978 0 41 1.38215488 2.98529412 11 RAC#made Single Kayak 0 -4.55238095 42 4.55238095 17:10 12 RACS made Double Kayak 571428571 0 55 1-30 4.78 13 R4Cmade Dinch 10 0 25 3.12307692 1130 14 15 Constraints 16 Final Shadow Constraint Allowable Allowable 27 Call Name Valur Price R.H. Side Increase Decrease 18 R11C7 Min Canon Total 79 2087912 50 29,2087912 JE 30 19 R1ZC Min Kayak Total 57.1428571 0 50 7.14285714 1E30 20 R13C7 Min Dinghy Total 10 3.12307692 30 49.962406 10 21 R6C7 Kayak mold Total 120 601465201 120 15.1212121 2.71111111 22 R7C7 Kayak oven Total 131428571 0 240 15.30 100.571429 23 R8C7 Kelvar Total 210 3.84615385 210 28 5142857 4.35714286 24 ROC? Finishing Total 242.098901 0 320 SE 30 77.9010089 25 R10C/ Fittings Total 320 15.6923077 320 3.45571429 19.4415584 27 28 Answer Report Sensitivity Report 1 Shecti 5) (4 pts] What is the production plan and total profit? Assume that fractional output is acceptable. If we force the variables to take integer values, then we cannot get a sensitivity report b) 14 pts] Which constraints are binding? c) (6 pts) Would the solution change if the minimum number of canoes made was increased to 60? if -the minimum number of kayaks was increased to 60% of the minimum number of dinghies was Increased to 202 d) (4 pts) it has been determined that the oven used to heat the kayak mold must be shut down in one month, leaving only 150 hours of time. Will this affect the solution or the profit? (Explain using the Riven output do not re-solve.) e) [4 pts] Extra fitting time can be obtained by hiring someone at minimum wage of $10.85. Should RBB hire someone? If so, for how many hours? 2 pts] Suppose they can also get someone to help with the kayak mold at $10.85 per hour. Should RBB hire someone? if so, for how many hours? 2) And suppose that they can also get someone to help with finishing at $10.85 per hour should RBB hire someone? If so, for how many hours? h) 12 pts) Management has noted that the plan calls for production of all products except the single kayak What would be the impact on profits if they decided to make a single kayak? 2 14 pts) Suppose that RBB has been able to obtain discounted costs on some material for cances such that the profit per small canoe increased to $34. Would this change their plan? And if the profit per regular canoe similarly increased to $43 would it change their plan? [4 pts] Dinghies are only being made because they have to deliver 10 of them. What would the profit per dinghy have to be to make RBB make them because they increased total profits? k). 17 pts] RBB has not made racing kayaks for many years, but still has the mold to produce them. To make a racing kayak, they would need 2.4 hours of mold prep time and 21 hours of mold oven time They would also need 2.1 hours of cutting/finishing time and 2.5 hours for installation of fittings How much profit would a racing kayak need to generate to make them profitable enough to consider? 1. Rose Bay Boatworks will be closing their facility in two months time so that major renovations can be done. They will be closed for almost 6 months and so want to make best use of resources that they have available before they close: R88 specializes in small watercraft, including canoes, kayaks, and dinghy's. These are made using two processes. The kayaks are made from polyethylene plastic that is heated in molds, whereas the other products are made from layers of fiberglass or Kevlar that are built in layers over a mold. In all cases after the basic watercraft shape is made, it requires some further cutting and finishing as well as the installation of fittings, inspection, and packaging. RBB formulated their problem as a linear program as follows: C1 = # of small canoes C2 = # of regular canoes K1 = # of one person kayaks K2 = # of two person kayaks D = # of dinghy's 22,861 + 2.3K2 Maximize Profit - $3201 + $4102 +S42K1 + $55K2 + $25D Subject to: Kayak mold prep time 2.0K1 + 2.1K2 Kayak oven time Kevlar/fiberglass time 2.201 + 2.5C2 Cutting/finishing time 1.5C1 + 1.5C2+1.8K1 - 2.0K2 Fitting installation time 1.5C1 + 2.0C2 +2.2K1 - 2.7K2 Minimum Canoe output C1+C2 Minimum Kayak output Kl. K2 Minimum Dinghy output D Non negativity C1, C2, K1, K2, D $ 120 hours s 240 hours + 1.6D S 210 hours +0.9D S 320 hours +1.40 S 320 hours 250 250 10 20 The Sensitivity Report is given below: 6 Variable Cells Final Reduced Objective Allowable Allowable B Cell Name Value Cost Coefficient increase Decres 9 R4C2 made Small Canoe 13:4055934 0 32 4.08 12162963 10 R4C3 # made Regular Cance 65.8021978 0 41 1.38215488 2.98529412 11 RAC#made Single Kayak 0 -4.55238095 42 4.55238095 17:10 12 RACS made Double Kayak 571428571 0 55 1-30 4.78 13 R4Cmade Dinch 10 0 25 3.12307692 1130 14 15 Constraints 16 Final Shadow Constraint Allowable Allowable 27 Call Name Valur Price R.H. Side Increase Decrease 18 R11C7 Min Canon Total 79 2087912 50 29,2087912 JE 30 19 R1ZC Min Kayak Total 57.1428571 0 50 7.14285714 1E30 20 R13C7 Min Dinghy Total 10 3.12307692 30 49.962406 10 21 R6C7 Kayak mold Total 120 601465201 120 15.1212121 2.71111111 22 R7C7 Kayak oven Total 131428571 0 240 15.30 100.571429 23 R8C7 Kelvar Total 210 3.84615385 210 28 5142857 4.35714286 24 ROC? Finishing Total 242.098901 0 320 SE 30 77.9010089 25 R10C/ Fittings Total 320 15.6923077 320 3.45571429 19.4415584 27 28 Answer Report Sensitivity Report 1 Shecti 5) (4 pts] What is the production plan and total profit? Assume that fractional output is acceptable. If we force the variables to take integer values, then we cannot get a sensitivity report b) 14 pts] Which constraints are binding? c) (6 pts) Would the solution change if the minimum number of canoes made was increased to 60? if -the minimum number of kayaks was increased to 60% of the minimum number of dinghies was Increased to 202 d) (4 pts) it has been determined that the oven used to heat the kayak mold must be shut down in one month, leaving only 150 hours of time. Will this affect the solution or the profit? (Explain using the Riven output do not re-solve.) e) [4 pts] Extra fitting time can be obtained by hiring someone at minimum wage of $10.85. Should RBB hire someone? If so, for how many hours? 2 pts] Suppose they can also get someone to help with the kayak mold at $10.85 per hour. Should RBB hire someone? if so, for how many hours? 2) And suppose that they can also get someone to help with finishing at $10.85 per hour should RBB hire someone? If so, for how many hours? h) 12 pts) Management has noted that the plan calls for production of all products except the single kayak What would be the impact on profits if they decided to make a single kayak? 2 14 pts) Suppose that RBB has been able to obtain discounted costs on some material for cances such that the profit per small canoe increased to $34. Would this change their plan? And if the profit per regular canoe similarly increased to $43 would it change their plan? [4 pts] Dinghies are only being made because they have to deliver 10 of them. What would the profit per dinghy have to be to make RBB make them because they increased total profits? k). 17 pts] RBB has not made racing kayaks for many years, but still has the mold to produce them. To make a racing kayak, they would need 2.4 hours of mold prep time and 21 hours of mold oven time They would also need 2.1 hours of cutting/finishing time and 2.5 hours for installation of fittings How much profit would a racing kayak need to generate to make them profitable enough to consider