Jansen Gas creates three types of aviation gasoline (avgas), labeled A, B, and C

Question

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?

Explanation / Answer

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?

If restriction is ignored, it would still get the same income. It is more convenient increased production of gasoline type B since this is more expensive and perhaps generate more revenue because they do not yet know if the high rate of TEL could offset the expenses and be equal to the gancia by selling gasoline type A.

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?

That would not be the best way to optimize revenue because the minimum octane number required for type gaolina B is 97 and reduce it would not be convenient for the customer, since this value is crucial for use according to compression who apply engines in cars for example when using this type of fuel.

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.

Of course, Decreased if Reid vapor pressure could optimize revenue due to the smaller amount of raw material needed in mixing to obtain each of the three types of fuel. But it is not possible to estimate the amount of extra revenue because of declining Reid vapor pressure with the data supplied.

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).

Well, you could increase the octane number to 108 corresponding to all of isopentane in the mixture rather than the presence of other substances. It is important to mention that to increase gasoline obtanaje in type A should increase the proportion of alkylate and isopentane in the mixture.

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?

Of course if all unit prices of the three grades of gasoline and all unit prices of raw materials increased by the same percentage optimal mixing remains the same as what is sought is compliance with especifiaciones you should get each one of the types of gasoline.

I hope my explanation has been useful for you.

Good luck!

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