One local hospital has just enough space and funds currently available to start either a cancer or heart research lab. If admini
stration decides on the cancer lab, there is a 20 percent chance of getting $100,000 in outside funding from the American Cancer Society next year, and an 80 percent chance of getting nothing. If the cancer research lab is funded the first year, no additional outside funding will be available the second year. However, if it is not funded the first year, then management estimates the chances are 50 percent it will get $100,000 the following year, and 50 percent that it will get nothing again. If, however, the hospital's management decides to go with the heart lab, then there is a 50 percent chance of getting $50,000 in outside funding from the American Heart Association the first year and a 50 percent chance of getting nothing. If the heart lab is funded the first year, management estimates a 40 percent chance of getting another $50,000 and a 60 percent chance of getting nothing additional the second year. If it is not funded the first year, then management estimates a 60 percent chance for getting $50,000 and a 40 percent chance for getting nothing in the following year. For both the cancer and heart research labs, no further possible funding is anticipated beyond the first two years.
Required:
1. What would be the total payoff if the heart lab were funded in both the first and second years?
Required:
1. What would be the total payoff if the heart lab were funded in both the first and second years?
1 answer:
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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
