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Solving for objective functions to maximize returns and probability of failures

(See attached file for full problem description)

1. The strategic Investment Corporation is developing a mix of investments to meet the needs of a clilent with one million dollars to invest. A mix of five investments are being considered, with data on each as shown below:

Investment Minimun Average Maximun
Investment Annual Investment
none A 10% 500,000
none B 12% 275,000
5,000 C 16% 250,000
10,000 D 14% 125,000
5,000 E 9% none

The total return must be at least 12.5% , all the money must be invested, and investments A and B together must not be over $700,000

A. What is the objective function assuming the corporation wants to maximize the return for it's client?

a. max z = 10x1+12x2+16x3+14x4+9x5
b. max z = .10x+.12x2+.16x3+.14x4+.09x5
c. max z = x1+x2+x3+x4+x5
d. max z = x1+X2+X3+X4+X5=125,000
e. max z = .61(x1+x2+x3+x4+x5)
B. What is the constraint corresponding to the total average return being at least 12.5 %?
a. x1+x2+x3+x4+x5>= 12.5
b. 12.5(x1+x2+x3+x4+x5)=100,000
c. .10x1+.12x2+.16x3+.14x4+.09x5>=125,000
d. 500x1+275x2+250x3+125x4=125,000
e. X1+x2+x3+x4+x5>=125,000

C. What is (are) the constraints regarding Investments. A and B together must not be over $700,000
a. x1<=(700,000: x2<=700,000
b. .22(x1+x2)<=700,000
c. 10x1+12x2<=700,000
d. X1+x2<700,000
e. .10x1+.12x2<=700,000

2. A company manufactures cellular phones for sale around the world. They are concerned about the reliability of three delicate electronic components (coded as a, b, c) that form a particular subsystem in the phones. They tested 100 units of each component for 50 hours and found that the following number of units failed. 3 for component A, 1 for Component B and 2 for component C.

a. What is the failure rate for component A.
a. .01
b. .02
c. .03
d. .04
e. .05

b. what is the reliability of component B?
c. what is the mean time between failures for component C?
d. What is the reliability for the electronic system?
3. A company that manufactures arrows for sale in archery stores is developing a new arrow with enhanced flight characteristics. From customer surveys the company has determined that the diameter of the arrow should be between 10.0 and 10.6 mm. They want to ensure the process they develop to produce the arrows will meet customer expectations; that is, the process capability index will be greater than or equal to 1.00

a. What value of the standard deviation of the process will yield a PCI equal to 1.00

a. .01
b. .05
c. .10
d. .20
e. .30

b. If the standard deviation of the process is actually .05, what would the diameter variation (ul - ll) of the arrow have to be to get a PCI of 1.00

a. .10
b. .30
c. .50
d. .60
e. .90


Solution Summary

Three probability and statistics questions dealing with objective functions, Standard deviation and failure rates.