Hello all,
I would appreciate it, if anyone could/would help me to solve a linear programming problem that belongs on the sub-category of investment planning.
The problem:
Airline examines the problem of buying new passenger jet
aircraft to enhance the aviation fleet. Past study
resulted in the selection of three types of aircraft:
Type A: Long-range, with purchase price of EUR 7 million
Type B: mid-range in price 5 million.
Type C: short-range in price 4 million.
It is envisaged that air transport will be large enough for all
distances to the planes of the company, regardless of type, used
essentially the maximum of their capacity. Under these conditions
estimated that the annual net profit, after the service of capital, the
depreciation and all other costs, will be:
0.5 million airplane type A
0.4 million airplane type B
0.3 million for aircraft type C
Also that the company will have enough pilots and staff to
Manning to 30 new aircraft.On the other hand if bought only short-range
aircraft, maintenance crews of the company can serve up to 50
new aircraft. Each aircraft type B, however, employs workshops twice as long
from one aircraft type C, and each plane type A twice as long from one aircraft
type B.
These calculations have resulted from preliminary analysis of
problem. While designed to be more detailed analysis, the administration of
company is now forced to choose between two potential funding.
The company can borrow freely to 100 million or
borrow with government guarantees up to 150 million euros.But In the second case,
State requires for national defense (use the aircraft for
transport in case of war),to purchase at least 5 aircraft type A.
It is assumed that the net profit for the company from each plane is the same
regardless of the mode of financing.
Sought to determine the optimal number of each type of aircraft to be
purchased both in the case of free financing and in
case of financing through government guarantee. It also sought to identify
maximum profits in each case,and choose the most beneficial backing.
Some thoughts, but not sure.
Set, number of type A Aircraft = x1 , number of type B = x2 , number of type C = x3
After that the objective function would be z= x1*0.5 + x2*0.4 + x3*0.3
1st restriction would be x1 + x2 + x3 <= 30
2nd x3<= 50
I can't ''decode'' the ''Each aircraft type B, however, employs workshops twice as long
from one aircraft type C, and each plane type A twice as long from one aircraft
type B.'' part of the problem.
Considering the type of funding I guess it will need to make 2 separate problems for the 100 and 150 million euros types of funding...
Any ideas,anyone?