Linear, Integer and Mixed Integer Programming
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 6.7 hours of wiring and 6.85 hours of drilling. Each fan must go through 4.95 hours of wiring and 5.65 hours of drilling. During the next production period, 310 hours of wiring time are available and up to 335 hours of drilling time may be used. Each air conditioner sold yields a profit of $75.70. Each fan assembled may be sold for a $55.95 profit.
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: 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 and fans produced in order to fulfill a contract to a good customer.
Question 3: If All Season decides that at least 32 air conditioners and 15 fans should be produced, what would be the optimal solution? Use the Excel template provided or the corner point method.
Question 4: 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, 2250 hours of wiring time are available, 70 hours of packing and up to 1590 hours of assembly time may be used. The following table presents the production requirements per unit:
Bill of Labor
|
Product
|
Wiring
|
Assembly
|
Packaging
|
|
Humidifiers
|
2.5 hrs.
|
3.25 hrs.
|
1.45 hrs.
|
|
Air Cleaners
|
1.75 hrs.
|
4.5 hrs.
|
1.0 hrs.
|
|
Fans
|
1.75 hrs.
|
2.9 hrs.
|
1.75 hrs.
|
Standard Costs
|
Product
|
Material
|
Labor
|
Overhead
|
Selling Price
|
|
Humidifiers
|
$23.50
|
$9.50
|
$28.50
|
$90.35
|
|
Air Cleaners
|
$28.15
|
$8.35
|
$19.75
|
$75.25
|
|
Fans
|
$8.55
|
$7.25
|
$11.25
|
$41.80
|
Question 5: 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 6: 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 20 humidifiers, and 15 air cleaners, which have to be made, additionally after checking the inventory decided that 10 additional fans should be made.
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: 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 have hired two additional people to work in the Packaging Department which adds 80 hours to the time available and the constraint that no more than 25 humidifiers could be produced:
Question 9: 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 10: 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
|
Wiring
|
Packaging
|
Material Handling
|
|
$13.25
|
$15.10
|
$9.75
|
$13.10
|
Additional investigation into manufacturing costs reveal that at least 20% of the man-hours must be allocated to performing material handling tasks, 50% must be allocated to wiring and assembly and 30% must be allocated to wiring and packaging. If a block of 55 man-hours is analyzed answer the following questions:
Question 11: 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 12: The prior analysis revealed a flaw in the data; the accountants ignored the constraint that a minimum of fifteen man-hours had to be allocated to Wiring. Formulate and develop a LP model accounting for this new constraint.
Question 13: 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 twelve man-hours. Formulate and develop a LP model accounting for this new constraint.