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For a device to

For a device to

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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116. For a device to work properly, three subsystems of the device must all function properly. To increase the reliability of the device, spare units may be added to each system. It costs 100 TL to add a spare unit to system 1, 300 TL to system 2, and 200 TL to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in Table. Use dynamic programming to maximize the probability that the device will work properly, given that 600 TL is available for spare units. Identify and explain decision variables, stages, states and formulate a recursion to design the device with optimal reliability. Probability that a system works system 1 Number of spares system 3 system 2 .60 .85 .70 1 .90 .85 .90 2 .95 .95 .98 117. You are planning on moving to a new house. You need to move n items of size aj , j-1,2,.,.n. You have bought m boxes (box i has size bi , i- 1,2,.,m). You need to rent a truck that will help fit all your items in it. There are two sizes of trucks to choose from: the smaller truck has a size of Qi and the larger truck has a size more than Qi. Since the rent of the smaller truck is cheaper, you would like to rent the smaller truck if the move is possible with it. Formulate an integer (or mixed integer) programming problem in order to decide whether the move is possible with a single trip of the smaller truck. Note that you can put multiple items in the same box and size is the only criterion determining if an item can be put into a box.
Transcribed Image Text:116. For a device to work properly, three subsystems of the device must all function properly. To increase the reliability of the device, spare units may be added to each system. It costs 100 TL to add a spare unit to system 1, 300 TL to system 2, and 200 TL to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in Table. Use dynamic programming to maximize the probability that the device will work properly, given that 600 TL is available for spare units. Identify and explain decision variables, stages, states and formulate a recursion to design the device with optimal reliability. Probability that a system works system 1 Number of spares system 3 system 2 .60 .85 .70 1 .90 .85 .90 2 .95 .95 .98 117. You are planning on moving to a new house. You need to move n items of size aj , j-1,2,.,.n. You have bought m boxes (box i has size bi , i- 1,2,.,m). You need to rent a truck that will help fit all your items in it. There are two sizes of trucks to choose from: the smaller truck has a size of Qi and the larger truck has a size more than Qi. Since the rent of the smaller truck is cheaper, you would like to rent the smaller truck if the move is possible with it. Formulate an integer (or mixed integer) programming problem in order to decide whether the move is possible with a single trip of the smaller truck. Note that you can put multiple items in the same box and size is the only criterion determining if an item can be put into a box.
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