Dave is not absolutely sure that the “side” constraint of at least as much gas A as gas B is necessary. What is this constraint costing the company? That is, how much more revenue could Jansen earn if this constraint were ignored? 2. Dave consults the chemical experts, and they suggest that gas B could be produced with a “medium” level of TEL. The octane ratings for each feedstock with this medium level would be halfway between their low and high TEL octane ratings. Would this be a better option in terms of its optimal revenue?
Atmospheric Pollution
In the atmosphere, the existence of large quantities of undesirable substances that could cause several health issues to living organisms and humans is atmospheric pollution. Air pollution is otherwise known to be atmospheric pollution. The presence of undesirable materials would also destruct the natural environment such as a change in climate, degradation of habitat, or depletion of ozone. Air pollution is generated by the natural processes and activities of humans.
Smokestack Scrubbers
Once we believe in the environment and remember the pollution-producing facets of it, we will consider the smoke-stacks scrubber to be a number of the worst offenders. Although this is often legally correct, smoke-stack scrubbers often have a big function in terms of keeping ground-level air pollutants- safe to breathe and assisting within the management of emissions.
Jansen Gas creates three types of aviation gasoline
(avgas), labeled A, B, and C. It does this by blending
four feedstocks: Alkylate; Catalytic Cracked
Gasoline; Straight Run Gasoline; and Isopentane.
Jansen’s production manager, Dave Wagner, has
compiled the data on feedstocks and gas types in
Tables 4.6 and 4.7. Table 4.6 lists the availabilities
and values of the feedstocks, as well as their key
chemical properties, Reid vapor pressure, and octane
rating. Table 4.7 lists the gallons required, the
prices, and chemical requirements of the three gas
types.
Table 4.6 Data on Feedstocks
Feedstock Alkylate CCG SRG Isopentane
Gallons available (1000s) 140 130 140 110
Value per gallon $4.50 $2.50 $2.25 $2.35
Reid vapor pressure 5 8 4 20
Octane (low TEL) 98 87 83 101
Octane (high TEL) 107 93 89 108
Table 4.7 Data on Gasoline
Gasoline A B C
Gallons required (1000s) 120 130 120
Price per gallon $3.00 $3.50 $4.00
Max Reid pressure 7 7 7
Min octane 90 97 100
TEL level Low High High
Note that each feedstock can have either a low
or a high level of TEL, which stands for tetraethyl
lead. This is measured in units of milliliters per gallon,
so that a low level might be 0.5 and a high level might
be 4.0. (For this problem, the actual numbers do not
matter.) As indicated in Table 4.6, the TEL level affects
only the octane rating, not the Reid vapor pressure.
Also, gas A is always made with a low TEL level,
whereas gas types B and C are always made with a
high TEL level.
As indicated in Table 4.7, each gasoline has two
requirements: a maximum allowable Reid vapor
pressure and a minimum required octane rating. In
addition to these requirements, the company wants
to ensure that the amount of gas A produced is at
least as large as the amount of gas B produced.
Dave believes that Jansen can sell all of the gasoline
it produces at the given prices. If any feedstocks
are left over, they can be sold for the values indicated
in Table 4.6. He wants to find a blending plan that
meets all the requirements and maximizes the revenue
from selling gasoline and leftover feedstocks. To help
Dave with this problem, you should develop an LP optimization
model and then use Solver to find the optimal
blending plan. Then, using this model as a starting
point, you should answer the following questions:
1. Dave is not absolutely sure that the “side” constraint
of at least as much gas A as gas B is necessary.
What is this constraint costing the company?
That is, how much more revenue could
Jansen earn if this constraint were ignored?
2. Dave consults the chemical experts, and they
suggest that gas B could be produced with a
“medium” level of TEL. The octane ratings for
each feedstock with this medium level would be
halfway between their low and high TEL octane
ratings. Would this be a better option in terms of
its optimal revenue?
3. Suppose that because of air pollution concerns,
Jansen might have to lower the Reid vapor pressure
maximum on each gas type (by the same
amount). Use SolverTable to explore how such a
change would affect Jansen’s optimal revenue.
4. Dave believes the minimum required octane rating
for gas A is too low. He would like to know
Case 4.1 Blending Aviation Gasoline at Jansen Gas 215
how much this minimum rating could be
increased before there would be no feasible
solution (still assuming that gas A uses the low
TEL level).
5. Dave suspects that only the relative prices matter
in the optimal blending plan. Specifically, he
believes that if all unit prices of the gas types
and all unit values of the feedstocks increase
by the same percentage, then the optimal
blending plan will remain the same. Is he
correct? ■
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