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Luck has two machines that analyze various blood samples. Recently, the demand for analyzing blood samples has increased and the lab director is planning to use linear programming to maximize the revenue for the lab. The lab gets blood samples for four types of special blood tests in the evening that must be completed the next day. The revenue from each type of special test and the time (in minutes) it takes on each machine is shown below. Revenue per test Time on Machinel Time on Machine 2 Test Type 1 $15 a. 3 minutes 5 minutes Test Type 2 $12 4 minutes 3 minutes C. What is the optimal solution? Test Type 3 $20 4 minutes 5 minutes. Any machine can be used to process any type of the tests. Every day, each machine can be used for 12 hours (720 minutes). If anytime is left over in any machine, the lab can do routine tests which take 3 minutes pertest on either machine and the lab earns a revenue of $9 per test. There are usually about 200 routine tests waiting to be done which could be done whenever the lab has time. This morning, the lab needs to complete 60 typel, 75 type 2, 70 type 3, and 50 type 4 tests. How many tests of each type should be done on each machine today? (Hint: 10 decision variables) Formulate the Integer Linear Programming model for this problem. Test Type 4 $18 5 minutes 4 minutes b. Create a spreadsheet model for this problem and solve it using Solver.

Luck has two machines that analyze various blood samples. Recently, the demand for analyzing blood samples has increased and the lab director is planning to use linear programming to maximize the revenue for the lab. The lab gets blood samples for four types of special blood tests in the evening that must be completed the next day. The revenue from each type of special test and the time (in minutes) it takes on each machine is shown below. Revenue per test Time on Machinel Time on Machine 2 Test Type 1 $15 a. 3 minutes 5 minutes Test Type 2 $12 4 minutes 3 minutes C. What is the optimal solution? Test Type 3 $20 4 minutes 5 minutes. Any machine can be used to process any type of the tests. Every day, each machine can be used for 12 hours (720 minutes). If anytime is left over in any machine, the lab can do routine tests which take 3 minutes pertest on either machine and the lab earns a revenue of $9 per test. There are usually about 200 routine tests waiting to be done which could be done whenever the lab has time. This morning, the lab needs to complete 60 typel, 75 type 2, 70 type 3, and 50 type 4 tests. How many tests of each type should be done on each machine today? (Hint: 10 decision variables) Formulate the Integer Linear Programming model for this problem. Test Type 4 $18 5 minutes 4 minutes b. Create a spreadsheet model for this problem and solve it using Solver.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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Luck has two machines that analyze various blood samples. Recently, the demand for analyzing blood samples has increased and the lab director is planning to use linear programming to maximize the revenue for the lab. The lab gets blood samples for four types of special blood tests in the evening that must be completed the next day. The revenue from each type of special test and the time (in minutes) it takes on each machine is shown below. Revenue per test Time on Machinel Time on Machine 2 Test Type 1 $15 a. 3 minutes 5 minutes Test Type 2 $12 4 minutes 3 minutes C. What is the optimal solution? Test Type 3 $20 4 minutes 5 minutes Any machine can be used to process any type of the tests. Every day, each machine can be used for 12 hours (720 minutes). If anytime is left over in any machine, the lab can do routine tests which take 3 minutes pertest on either machine and the lab earns a revenue of $9 per test. There are usually about 200 routine tests waiting to be done which could be done whenever the lab has time. This morning, the lab needs to complete 60 typel, 75 type 2, 70 type 3, and 50 type 4 tests. How many tests of each type should be done on each machine today? (Hint: 10 decision variables) Formulate the Integer Linear Programming model for this problem. Test Type 4 $18 5 minutes 4 minutes b. Create a spreadsheet model for this problem and solve it using Solver.
Transcribed Image Text:Luck has two machines that analyze various blood samples. Recently, the demand for analyzing blood samples has increased and the lab director is planning to use linear programming to maximize the revenue for the lab. The lab gets blood samples for four types of special blood tests in the evening that must be completed the next day. The revenue from each type of special test and the time (in minutes) it takes on each machine is shown below. Revenue per test Time on Machinel Time on Machine 2 Test Type 1 $15 a. 3 minutes 5 minutes Test Type 2 $12 4 minutes 3 minutes C. What is the optimal solution? Test Type 3 $20 4 minutes 5 minutes Any machine can be used to process any type of the tests. Every day, each machine can be used for 12 hours (720 minutes). If anytime is left over in any machine, the lab can do routine tests which take 3 minutes pertest on either machine and the lab earns a revenue of $9 per test. There are usually about 200 routine tests waiting to be done which could be done whenever the lab has time. This morning, the lab needs to complete 60 typel, 75 type 2, 70 type 3, and 50 type 4 tests. How many tests of each type should be done on each machine today? (Hint: 10 decision variables) Formulate the Integer Linear Programming model for this problem. Test Type 4 $18 5 minutes 4 minutes b. Create a spreadsheet model for this problem and solve it using Solver.
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