3. Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints: a. 3A + 2B -s 18 b. 12A + 8B 2: 480 c. SA + lOB = 200 9. Identify the feasible region for the foll~wing ~et of constraints: . 3A-2B2: 0 2A - IB :S200 lA -s ISO A,B>O 1L Solve the following linear program using the graphical solution procedure: Max s.t, SA + SB lA :s 100 IB:S 80 2A + 4B:s 400 A,B>O IS. Suppose that Par's management (problem 14) encounters the following situations: a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag. b. A new low-cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.) c. New sewing equipment is available that would increase the sewing operation capacity to 7S0 hours. (Assume that lOA + 9B is the appropriate objective function.) If each of these situations is encountered separately, what is the optimal solution and the total rofit contribution? 23. Embassy Motorcycles (EM) manufacturers two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy's motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 280 Lady-Sport frames for the next production period: Final assembly and testing requires 2 hours for each EZ-Rider model and 2.S hours for each Lady-Sport modeL A maximum of 1000 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2400 for each EZ-Rider produced and $1800 for each Lady-Sport produced. a. Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution b. c. to profit. Solve the problem graphically. What is the optimal solution? Which constraints are binding? 3. 9. Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints: a. 3A + 2B:5 18 b. 12A + 8B:2: 480 c. SA + lOB = 200 Identify the feasible region for the follo~ing set of constraints: . 3A - 2B:2: 0 2A - IB :5200 lA :51S0 A,B>O 11. Solve the following linear program using the graphical solution procedure: Max s.t, SA + SB lA :5 100 IB:5 80 2A + 4B:5 400 A,B>O IS. Suppose that Par's management (problem 14) encounters the following situations: a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag. b. A new low-cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.) c. New sewing equipment is available that would increase the sewing operation capacity to 7S0 hours. (Assume that lOA + 9B is the appropriate objective function.) If each of these situations is encountered separately, what is the optimal solution and the total rofit contribution? 23. Embassy Motorcycles (EM) manufacturers two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy's motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 280 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model and 2.S hours for each Lady-Sport model. A maximum of 1000 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2400 for each EZ-Rider produced and $1800 for each Lady-Sport produced. a. Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to profit. b. Solve the problem graphically. What is the optimal solution? c. Which constraints are binding