Bearland Manufacturing produces 4 different types of wood paneling. Each type of paneling is made by gluing and pressing

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Bearland Manufacturing produces 4 different types of wood
paneling. Each type of paneling is made by gluing and pressing
together a different mixture of pine and oak chips. The following
table summarizes the required amount of gluing, pressing, and
mixture of wood chips required to produce a pallet of 50 units of
each type of paneling:
Assume the company has 6,000 quarts of glue; 7,500 hours of
pressing capacity; 30,000 pounds of pine chips; and 62,500 pounds
of oak chips available in the next production cycle. Further assume
that each pallet of Tahoe, Pacific, Savannah, and Aspen panels can
be sold for profits of $460, $1,160, $790, and $390, respectively.
Finally, for marketing purposes, the company wants to produce at
least 4 pallets of each type of paneling.
Formulate an LP model, then use Solver to create a Sensitivity
Report for your model and answer the following questions.
(a)
Is the solution degenerate?
(b)
Is the solution unique?
Some of the allowable increase or decrease values for the
objective coefficients are zero, so there are alternate optimal
solutions.
None of the allowable increase or decrease values for the
objective coefficients are zero, so the optimal solution is
unique.
We cannot determine if the optimal solution is unique based on
our sensitivity report because the solution is degenerate.
Some of the allowable increase or decrease values for the RHS
values are zero, so there are alternate optimal solutions.
None of the allowable increase or decrease values for the RHS
values are zero, so the optimal solution is unique.
(c)
Suppose the profit per pallet of Tahoe panels went down by $55.
Would the optimal solution change?
(d)
Suppose the profit per pallet of Aspen panels went up by $40.
Would the optimal solution change?
(e)
At most, how much should the company be willing to pay (in
dollars) to obtain 1,200 additional hours of pressing
capacity? (If it is not worth it to pay for this much additional
pressing capacity, enter NA. Round your answer to two decimal
places.)
(f)
Suppose the company has received an offer to
buy 5,100 pounds of its pine chips for $1,480. Should it
accept this offer? Explain your answer. (Give your answer in
dollars. Round your answer to two decimal places.)
Since $1,480 is less or greater than the amount profit
would be reduced if 5,100 pounds of pine chips were
removed, $ , it makes or does not
make sense for the company to accept this offer.
(g)
Create a Spider Plot illustrating how the optimal profit changes
as the availability of each of the four resources varies from 90%
to 110% of their given values. Explain the relationship between
this graph and the shadow prices of the resources given on the
sensitivity report.
As the RHS constraint increases, the profit appears to increase
for resources with lower shadow prices and decrease for resources
with higher shadow prices.
As the RHS constraint increases, the profit appears to decrease
for resources with lower shadow prices and increase for resources
with higher shadow prices.
The profit appears to be more sensitive to changes in resources
with lower shadow prices.
The profit appears to be more sensitive to changes in resources
with higher shadow prices.The profit appears to not change at all
for resources with shadow prices less than 1.
(h)
Suppose there in some uncertainty about the amount of pressing
capacity that might be available. Create a Solver Table report
summarizing how the optimal solution and profit changes as the
amount of pressing capacity available changes from 5,000 to 7,000
in increments of 500. What information does this report convey
about the optimal product mix as a function of the available
pressing capacity?
As pressing capacity increases from 5,000 to 7,000, the optimal
number of Tahoe pallets, stays the same increases then
decreases decreases increases decreases then
increases , the optimal number of Pacific pallets ,stays
the same increases then
decreases decreases increases decreases then
increases , the optimal number of Savannah
pallets, stays the same increases then
decreases decreases increases decreases then
increases , and the optimal number of Aspen
pallets, stays the same increases then
decreases decreases increases decreases then
increases