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# HW1 - IE 505 Homework#1 Question 1 Fiyat Auto-Modification...

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IE 505 Homework #1 Question 1 Fiyat Auto-Modification Company deals with modification of specific car engines. A modification lover John Carter comes to the Fiyat Auto-Modification 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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HW1 - IE 505 Homework#1 Question 1 Fiyat Auto-Modification...

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