MBA 6300 online Homework Assignment #5 Linear Programming Models Instructions: After the student calculates the answers to this homework he/she must submit the answers by placing them in the Assignment # _ Submittal Link in Bb by midnight of the date shown in the Course Roadmap and Syllabus. The Instructor does not allow late submissions therefore a score of zero (0) will be recorded for the assignment if submitted after midnight Eastern Time of the due date. Solutions for the assignment will be released in Bb the morning after the due date for access by students. Total points for the assignment is 85. Note: There is no partial credit given; either the answer is correct or incorrect. After you have submitted your answers in the Assignment #_ Submission Link, upload the Excel file (provided you by the Instructor) containing your answers and calculations into the Home Work #_ Supporting Documentation Submission link prior to the due date and time. As stated in the syllabus a score of zero will be awarded for the assignment if this Excel file is not submitted. NOTE: UNLESS EXPRESSLY STATED CARRY YOUR ANSWERS TO TWO (2) DECIMAL PLACES. Scenario 1: The All Season Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 6.15 hours of wiring and 4.75 hours of drilling. Each fan must go through 4.15 hours of wiring and 5.25 hours of drilling. During the next production period, 250 hours of wiring time are available and up to 300 hours of drilling time may be used. Each air conditioner sold yields a profit of $72.70. Each fan assembled may be sold for a $49.50 profit. (5 points each for a total of 15 points) Question 1: Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans and that yields the highest profit. Feel free to use the Excel template provided or the corner point method. Question 2: Identify the binding constraint of the model. Question 3: Round your Solution Values to a whole number and calculate the profit using the rounded solution. Scenario 2: All Season's management realizes that it forgot two critical constraints (see Question #1 above). In particular, management decides that there should be a minimum number of air conditioners produced in order to fulfill a contract to a good customer. Also, due to the cancelation of an order in the preceding period there is an oversupply of fans, therefore a limit should be placed on the total number of fans produced. (5 points each for a total of 15 points) Question 4: If All Season decides that at least 30 air conditioners should be produced but no more than 15 fans should be produced, what would be the optimal solution? How much Dr. Mike's MBA 6300 Homework #5 Page 1 slack is there for each of the four constraints? Use the Excel template provided or the corner point method. Question 5: Identify the binding constraint of the model. Question 6: Round your Solution Values to a whole number and calculate the profit using the rounded solution. Scenario 3: The ABC Corporation manufactures three electrical products; humidifiers, fans and air cleaners. The manufacturing process is composed of three processes: wiring, packaging and assembly. During the next production period, 2000 hours of wiring time are available, 60 hours of packing and up to 1500 hours of assembly time may be used. The following table presents the production requirements per unit: (5 points each for a total of 15 points) Bill of Labor Product Humidifiers Air Cleaners Fans Standard Costs Product Humidifiers Air Cleaners Fans Wiring 2 hrs. 1 hrs. 1.25 hrs. Material $17.50 $26.15 $6.55 Assembly 3 hrs. 4 hrs. 2.1 hrs. Labor $7.50 $6.35 $4.75 Overhead $26.45 $19.75 $9.55 Packaging 1.25 hrs. 0.75 hrs. 1.50 hrs. Selling Price $75 $70 $36.25 Question 7: Formulate and solve this LP production mix situation to find the best combination of air conditioners, humidifiers and fans and that yields the highest profit. Feel free to use the Excel template provided or the corner point method. Question 8: Identify the binding constraint of the model. Question 9: Round your Solution Values to a whole number and calculate the profit using the rounded solution. Scenario 4: Management did not like the solution presented in Scenario 3 above and, based on its open order file, placed additional constraints on the model. First there was an open order for at least 10 humidifiers, and 12 air cleaners, which have to be made, additionally after checking the inventory decided that no more than 20 fans should be made. (5 points each for a total of 15 points) Question 10: Formulate and solve this LP production mix situation to find the best combination of air conditioners, humidifiers and fans and that yields the highest profit. Feel free to use the Excel template provided or the corner point method. Question 11: Identify the binding constraint of the model. Dr. Mike's MBA 6300 Homework #5 Page 2 Question 12: Round your Solution Values to a whole number and calculate the profit using the rounded solution. Scenario 5: Using the data and constraints presented in Scenarios 3 & 4 and the fact that you were not comfortable with the calculated solution for the number of fans to produce you have added an additional constraint that a minimum of 10 fans must be produced: (5 points each for a total of 10 points) Question 13: Formulate and solve this LP production mix situation to find the best combination of air conditioners, humidifiers and fans and that yields the greatest profit. Feel free to use the Excel template provided or the corner point method. Question 14: Round your Solution Values to a whole number and calculate the cost using the rounded solution. Scenario 6: The ABC Corporation management has hired a cost accountant to make some recommendations regarding the cost allocation of labor used to produce air cleaners. The average wages of personnel performing particular processes are presented in the table below. Assembly $12.75 Wiring $14.50 Packaging $9.25 Material Handling $13.50 Additional investigation into manufacturing costs reveal that at least 15% of the manhours must be allocated to performing material handling tasks, 45% must be allocated to wiring and assembly and 30% must be allocated to wiring and packaging. If a block of 50 manhours is analyzed answer the following questions: (5 points each for a total of 15 points) Question 15: Formulate and develop a LP model to find the best combination of labor hours and that yields the lowest cost. Feel free to use the Excel template provided or the corner point method. Question 16: The prior analysis revealed a flaw in the data; the accountants ignored the constraint that a minimum of twelve (12) manhours had to be allocated to Wiring. Formulate and develop a LP model accounting for this new constraint. Question 17: The prior analysis revealed another flaw in the analysis; the accountants failed to identify that packaging is over allocated thus they want to add another constraint stating that packaging must be allocated a maximum of ten (10) manhours. Formulate and develop a LP model accounting for this new constraint. Dr. Mike's MBA 6300 Homework #5 Page 3