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 samepercentage, then the optimal blending plan will remain the same. Is he correct?

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  1. 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 samepercentage, then the optimal blending plan will remain the same. Is he correct?
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:
Transcribed Image Text: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:
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
ble 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
Transcribed Image Text: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 ble 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
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