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A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a
Chapter 3, Problem 3.2-19(choose chapter or problem)
A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters \(\alpha = 3\), \(\theta = 0.5\), where \(\theta\) is in units of days per 1000 units of rolls. It costs $2 to make a unit that sells for $5 on the first day when the rolls are fresh. Any leftover units are sold on the second day for $1. How many units should be made to maximize the expected value of the profit?
Questions & Answers
QUESTION:
A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters \(\alpha = 3\), \(\theta = 0.5\), where \(\theta\) is in units of days per 1000 units of rolls. It costs $2 to make a unit that sells for $5 on the first day when the rolls are fresh. Any leftover units are sold on the second day for $1. How many units should be made to maximize the expected value of the profit?
ANSWER:Step 1 of 3
Given:
The variable X represents the demand(in 1000 units) for rolls.
The variable X has a gamma distribution with parameters 
It costs $2 to make a unit that sells for $5 on the first day when the rolls are fresh. Any leftover units are sold on the second day for $1.