A particular computer company has 12 sales reps based in New

A particular computer company has 12 sales reps based in New York City and 18 sales reps based in San Fransisco. To staff two upcoming trade shows the company wishes to send atleast 15 sales reps to the show in Dallas and atleast 10 reps to the show in Chicago. A minimum of 5 reps from the San Francisco office must be in Dallas. Round trip airfare is as follows:

New York to Dallas: $280   San Francisco to Dallas: $340

New York to Chicago: $160 San Fransisco to Chicago: $180

The objective is to minimize the total airfire cost while still satisfying the staffing requirements.

What is the objective function for this problem?

Solution

Objective function

Z = Min(cost of 10 people going to dallas and 15 to chicago)

The number of staff available in New York = 12

Staff available in San Fransisco = 18

Staff required in Dallas = 15

Staff required in Chicago = 10

5 reps must leave from the san fracisco office i.e. the cost of this thing will be equal to

=> 5 * 340 = 1700$

10 people can join dallas from the new york office (since the ticket is cheaper available)

=> 10 * 280 = 2800$

10 reps should go in chicago

=> 2 * 160 (since cost is less) + 8 * 180

=> 1760$

Total cost = 1700 + 1760 + 2800 = 6260$