The XYZ Company is considering a recreation project to enable the company to beg
ID: 2946426 • Letter: T
Question
The XYZ Company is considering a recreation project to enable the company to begin new financial projects. The company’s president must determine whether to make the expansion a small, medium- or large-scale project. Human resource’s salaries for the new financial projects is uncertain, which may be low salary, medium salary, or high salary. The probability estimates for salaries are .30, .45, and .25, respectively. Letting x,y and z indicate the annual cost in thousands of dollars, the firm’s human resource has for the small, medium- and large-scale expansion projects.
Salary
Low Scale
Medium Scale
Large Scale
X
F(x)
y
F(y)
z
F(z)
Low
35
0.3
42
0.3
50
0.3
Medium
65
0.45
68
0.45
75
0.45
High
82
0.25
90
0.25
110
0.25
a. Compute the expected value for the cost associated with the three expansion alternatives. Which decision is preferred for the objective of minimizing the expected cost?
b. Compute the variance for the cost associated with the three expansion alternatives. Which decision is preferred for the objective of minimizing the risk or uncertainty?
Salary
Low Scale
Medium Scale
Large Scale
X
F(x)
y
F(y)
z
F(z)
Low
35
0.3
42
0.3
50
0.3
Medium
65
0.45
68
0.45
75
0.45
High
82
0.25
90
0.25
110
0.25
Explanation / Answer
Solution
a. Expected cost :
Low scale i.e. E(X) = 35*0.3 + 65*0.45 + 82*0.25 = 60.25
E(Medium scale) = 42*0.3 + 68*0.45 + 90*0.25 = 65.7
E(Large scale) = 50*0.3 + 75*0.45+ 110*0.25 = 76.25
cost is minimum for low scale
b. variance :
Vx = E(X2) - E(X)2 = 3949.75 - 3630.0625 = 319.69
Vy = 4635 - 4316.49 = 318.51
vz = 6306.25 - 5814.0625 = 492.19
decision : medium scale
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