Northwoods Backpackers is a retail catalog store in Vermont that specializes in outdoor clothing and camping equipment. Phone orders are taken each day by a large pool of computer operators, some of whom are permanent and some temporary. A permanent operator can process an average of 76 orders per day, whereas a temporary operator can process an average of 53 orders per day. The company averages at least 600 orders per day. The store has 10 computer workstations. A permanent operator processes about 1.3 orders with errors each day, whereas a temporary operator averages 4.1 orders with errors daily. The store wants to limit errors to 24 per day. A permanent operator is paid $81 per day, including benefits, and a temporary operator is paid $50 per day. The company wants to know the number of permanent and temporary operators to hire to minimize costs.

Formulate an integer programming model for this problem and solve it by using the computer.

The minimum cost ( Z ) will be = $636 per day

number of permanent operators = 6

number of temporary operators = 3

Explanation:

considering the information given: the company has ten (10) workstations and also uses both permanent and temporary operators below is the detailed job that can be achieved with this resources

Orders per day

permanent operator ; 76

temporary operator ; 53

company average : (minimum ) 600

Errors per day

permanent operator ; 1.3

temporary operator ; 4.1

average allowable error : maximum ( 24 )

pay per day ; permanent ( $81 ), temporary ( $50 )

creating an integer program model for this problem of finding the number of permanent and temporary operators to hire to minimize costs

Assume number of permanent operators to be X1  and temporary operators to be X2

cost of operators per day would be ( Z ) = 81 X1 + 50 X2  ( first constraint )

workstations to be used by operators = X1 + X2 ≤ 10 (second constraint )

Total number of processed order by operators = 76 X1 + 53 X2 ≥ 600 (third)

allowable errors by the company = 1.3 X1 + 4.1 X2 ≤ 24 ( fourth constraint )

The number of operators must be an Integer = X1 , X2 ≥ 0 ( fifth constraint )

create an excel linear program using both the details given and also the applying the constraints created.

The minimum cost ( Z ) will be = $636 per day

number of permanent operators = 6

number of temporary operators = 3

attached is a snapshot of the final excel linear program

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