IE 505
–
Homework #1
Question 1
Fiyat AutoModification Company deals with modification of specific car engines. A modification
lover John Carter comes to the Fiyat AutoModification Center in order to get his C cars modified. But
he will not do all the modifications in a single year; he will do this among T years.
Each car i has an initial horsepower of HP
i
. The modification has a cost of $C
i
per horsepower (hp)
gain for car i. The modifications can be applied at fractional amounts. FIYAT does not increase the hp
of the cars more than %40 of the initial hp of the car. Of course, there are some consequences for
increasing the horsepower for the cars.
The main consequence is the fuel consumption. Each car i has initial (average) fuel consumptions of
FC
i
per 100kms. For 1 hp increase the fuel consumption increases by I
i
lt for car i.
The cars that are going to be modified have petrol and diesel engines. The first M (<C) cars have a
petrol engine whereas the rest of the cars have diesel engines. Since modification increases hp, the
consumption of fuel increases hence the unit price of each fuel type has a significant importance for
John Carter. John has some forecasts on unit price of petrol and diesel for each year: D
t
and P
t
respectively.
John Carter has budgets of $BI
t
for the modification operations for year t.
John always asks FIYAT Co. to do the modifications in the 1
st
of January. For each car that is going to
be modified, expected yearly usage amount is known and this is given by U
i,t
. John also knows that
his fuel consumption cannot exceed a budget of BU
t
for year t.
.
Note that John cannot spend any of his leftover budgets for the next years.
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 Spring '10
 zeynephuygur
 Internal combustion engine, Diesel engine, john carter, coffee shell

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