The demand for a product of Gippsland industries varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company's monthly demand Unit demand 300 400 500 600 Probability 0.20 0.30 0.35 0.15 (a) If the company places monthly orders based on the expected value of the monthly demand, what should Gippsland's monthly order quantity be for this period? Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or loss in a month if it places an order based on your answer to part (a) and where the actual demand for the item is 300 units? What is the standard deviation for the number of units demanded? (b) (c)
The demand for a product of Gippsland industries varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company's monthly demand Unit demand 300 400 500 600 Probability 0.20 0.30 0.35 0.15 (a) If the company places monthly orders based on the expected value of the monthly demand, what should Gippsland's monthly order quantity be for this period? Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or loss in a month if it places an order based on your answer to part (a) and where the actual demand for the item is 300 units? What is the standard deviation for the number of units demanded? (b) (c)
A First Course in Probability (10th Edition)
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Transcribed Image Text:the standard deviation of X.
The demand for a product of Gippsland industries varies greatly from month to month.
Based on the past two years of data, the following probability distribution shows the
company's monthly demand
2.
Unit demand
300
400
500
600
Probability
0.20
0.30
0.35
0.15
(a)
If the company places monthly orders based on the expected value of the monthly
demand, what should Gippsland's monthly order quantity be for this period?
Assume that each unit demanded generates $70 in revenue and that each unit
ordered costs $50. How much will the company gain or loss in a month if it places
an order based on your answer to part (a) and where the actual demand for the
item is 300 units?
What is the standard deviation for the number of units demanded?
(b)
(c)
Consider the state of the economy. There are three possible changes in the economy
between this year and next. For each type of change the probability and likely return are
given in the following table.
3.
Return if state occurs(x)
Probability of State p(x)
0.25
State of Economy
Recession
-0.05
Stable
0.5
0.15
D Focus
(25
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