You are the traffic manager for Fly-by-Night Airlines, which flies airplanes fro

Question

You are the traffic manager for Fly-by-Night Airlines, which flies airplanes from five cities: Los Angeles, Chicago, Atlanta, New York, and Boston. Due to strike, you have not had sufficient crews to fly your planes, so some of your planes have been stranded in Chicago and in Atlanta. In fact, 15 extra planes are in Chicago and 30 extra planes are in Atlanta. Los Angeles needs at least 10 planes to get back on schedule, New York needs at least 20, and Boston needs at least 10. It costs $50,000 to fly a plane from Chicago to Los Angeles, $10,000 to fly from Chicago to New York, and $20,000 to fly from Chicago to Boston, and $50,000 to fly from Atlanta to Boston. How should you rearrange your planes to get back on schedule at the lowest cost? What is the minimum cost?

Remember to start by identifying the unknowns. You need to decide how many planes you will fly from each of Chicago an Atlanta to each of Los Angeles, New York, and Boston. This gives you six unknowns:

1) Let a=

Let b=

Let c=

Let d=

Let e=

Let f=

2) Formulate the problem as a linear programming problem with an objective function and constraints.

Problem Constraint 1 (Los Angeles needs):

Problem Constraint 2 (New York needs):

Problem Constraint 3 (Boston needs):

Problem Cnstraint 4 (Chicago can provide):

Problem Constraint 5(Atlanta can provide):

Nonnegative Constraints:

Objective function (related to costs; a max or a min?):

Explanation / Answer

x = the number of planes to y from Chicago to LA
y = the number of planes to y from Chicago to NY
z = the number of planes to y from Chicago to Boston
u = the number of planes to y from Atlanta to LA
v = the number of planes to y from Atlanta to NY
w = the number of planes to y from Atlanta to Boston

  
Los Angeles needs at least 10 planes to get back on schedule
x+u >= 10 (1)
New York needs at least 20
y+v >= 20 (2)
and Boston needs at least 10
z+w >= 10 (3)

you have 15 extra planes in Chicago
x+y+z <= 15 (4)
and 30 extra planes in Atlanta
u+v+w <= 30 (5)

x,y,z,u,v,w > = 0

Minimize 5x + y + 2z + 7u + 2v + 5w *(10000)

It can be solved by Solver add in Excel ,

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