Northwoods Backpackers is a retail catalog store in Vermont that specializes in outdoor clothing and camping equipment. Phone or
ders 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.
Formulate an integer programming model for this problem and solve it by using the computer.
1 answer:
Answer:
The lowest cost ( Z ) will equal $636 daily
quantity of permanent operators = 6
quantity of temporary operators = 3
Explanation:
based on the provided information: the organization has a total of ten (10) workstations and employs both permanent and temporary operators; the following demonstrates the work that can be performed with these resources
Orders processed each day
permanent operator; 76
temporary operator; 53
company average: minimum of 600
Errors recorded daily
permanent operator; 1.3
temporary operator; 4.1
acceptable maximum error rate: 24
daily wages; permanent ($81), temporary ($50)
formulate an integer programming model to ascertain the number of permanent and temporary operators needed to minimize costs
Let X1 represent the permanent operators and X2 represent the temporary operators
the daily operator cost can be expressed as ( Z ) = 81 X1 + 50 X2 (first constraint)
operators at workstations = X1 + X2 ≤ 10 (second constraint)
Total orders handled = 76 X1 + 53 X2 ≥ 600 (third)
allowable errors permit = 1.3 X1 + 4.1 X2 ≤ 24 (fourth constraint)
Operators must be whole numbers = X1, X2 ≥ 0 (fifth constraint)
construct an Excel linear program incorporating both the data provided and the constraints formulated.
The lowest cost ( Z ) will equal $636 daily
quantity of permanent operators = 6
quantity of temporary operators = 3
included is a screenshot of the completed Excel linear program
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