(a)Formulate a model for the problem. For the second model, use subscripted variables named I for the inputs, O for the outputs, and X for the transferred amounts.
(b) Solve the model using Excel.
The blending operation has a capacity of 1,000,000 litres/day overall. Subject to the overall capacity, up to 500,000 litres/day of any input, or 650,000 litres/day of any output can be handled.
We can assume that there are no losses in the blending process, and that the characteristics of the outputs are a weighted average (by volume) of the characteristics of the inputs.
An gasoline blending operation has three types of inputs, with the following prices and characteristics:
|
Input
|
Price per litre
|
Octane Rating
|
Vapour (kPa)
|
|
1
|
$0.72
|
84
|
56
|
|
2
|
$0.80
|
93
|
48
|
|
3
|
$0.85
|
109
|
37
|
The inputs are blended to produce two outputs, with the following outputs and promised specifications:
|
Output
|
Price
|
Min. Octane rating
|
Max Vapour (kpa)
|
|
1
|
$0.83
|
86
|
54
|
|
2
|
$0.91
|
95
|
39
|