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. (5 points each for
a total of 10 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: 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. (5 points each for a total of
10 points)
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, 70hours of packing and up to 1590 hours of
assembly time may be used. The following table presents the production
requirements per unit: (5 points each for a total of 10 points)
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. (5 points each for a total of 10 points)
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: (5 points each for a total of 10 points)
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: (5 points each for a total of 15
points)
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
(15) 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 (12) man-hours. Formulate and develop a LP
model accounting for this new constraint.
