8 Allbest airlines has 100 planes. Planes break down an average of twice a year and take one week to fix. Assuming the times between breakdowns and repairs are exponential, how many repairmen are needed to ensure that there is at least a 95% chance that 90 or more planes are available? (Hint: Use a one-way data table.)

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8 Allbest airlines has 100 planes. Planes break down an
average of twice a year and take one week to fix. Assuming
the times between breakdowns and repairs are exponential,
how many repairmen are needed to ensure that there is at
least a 95% chance that 90 or more planes are available?
(Hint: Use a one-way data table.)
9 An army has 200 tanks. Tanks need maintenance 10
times per year, and maintenance takes an average of 2 days.
The army would like to have an average of at least 180 tanks
working. How many repairmen are needed? Assume
exponential interarrival and service times. (Hint: Use a one-
way data table.)
Group C
10 Bectol, Inc. is building a dam. A total of 10 million cu
ft of dirt is needed to construct the dam. A bulldozer is used
to collect dirt for the dam. Then the dirt is moved via dumpers
to the dam site. Only one bulldozer is available, and it rents
for $100 per hour. Bectol can rent, at $40 per hour, as many
dumpers as desired. Each dumper can hold 1,000 cu ft of
dirt. It takes an average of 12 minutes for the bulldozer to
load a dumper with dirt, and each dumper an average of five
minutes to deliver the dirt to the dam and return to the
bulldozer. Making appropriate assumptions about exponen-
tiality, determine how Bectol can minimize the total expected
cost of moving the dirt needed to build the dam. (Hint: There
is a machine repair problem somewhere!)
Transcribed Image Text:8 Allbest airlines has 100 planes. Planes break down an average of twice a year and take one week to fix. Assuming the times between breakdowns and repairs are exponential, how many repairmen are needed to ensure that there is at least a 95% chance that 90 or more planes are available? (Hint: Use a one-way data table.) 9 An army has 200 tanks. Tanks need maintenance 10 times per year, and maintenance takes an average of 2 days. The army would like to have an average of at least 180 tanks working. How many repairmen are needed? Assume exponential interarrival and service times. (Hint: Use a one- way data table.) Group C 10 Bectol, Inc. is building a dam. A total of 10 million cu ft of dirt is needed to construct the dam. A bulldozer is used to collect dirt for the dam. Then the dirt is moved via dumpers to the dam site. Only one bulldozer is available, and it rents for $100 per hour. Bectol can rent, at $40 per hour, as many dumpers as desired. Each dumper can hold 1,000 cu ft of dirt. It takes an average of 12 minutes for the bulldozer to load a dumper with dirt, and each dumper an average of five minutes to deliver the dirt to the dam and return to the bulldozer. Making appropriate assumptions about exponen- tiality, determine how Bectol can minimize the total expected cost of moving the dirt needed to build the dam. (Hint: There is a machine repair problem somewhere!)
6 For the machine repair model, show that W
KIĀ – (1/1).
7 (Requires use of a spreadsheet or LINGO) The machine
repair model may often be used to approximate the behavior
of a computer's CPU (central processing unit). Suppose that
20 terminals (assumed to always be busy) feed the CPU.
After the CPU responds to a user, he or she takes an average
of 80 seconds before sending another request to the CPU
(this is called the think time). The CPU takes an average of
Transcribed Image Text:6 For the machine repair model, show that W KIĀ – (1/1). 7 (Requires use of a spreadsheet or LINGO) The machine repair model may often be used to approximate the behavior of a computer's CPU (central processing unit). Suppose that 20 terminals (assumed to always be busy) feed the CPU. After the CPU responds to a user, he or she takes an average of 80 seconds before sending another request to the CPU (this is called the think time). The CPU takes an average of
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