The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable with probability mass function Px (0) 12 Px(1) = %3D 12 3 Px(2) = %3D 12 4 Px(3) = 12 2 Px(4) = 12 1 Px(5) = %3D 12 He also knows that there is a profit of $1.00 on each cake that he sells and a loss (due to spoilage) of $0.30 on each cake that he does not sell. Assuming that each cake can be sold only on the day it is made, how many chocolate cakes should he bake to maximize his expected profit? Windows buiü I| ||

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The manager of a bakery knows that the number of chocolate cakes he can sell on
any given day is a random variable with probability mass function
Px (0)
12
Px(1) =
%3D
12
3
Px(2) =
%3D
12
4
Px(3) =
12
2
Px(4) =
12
1
Px(5) =
%3D
12
He also knows that there is a profit of $1.00 on each cake that he sells and a loss
(due to spoilage) of $0.30 on each cake that he does not sell. Assuming that each
cake can be sold only on the day it is made, how many chocolate cakes should he
bake to maximize his expected profit?
Windows buiü
I| ||
Transcribed Image Text:The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable with probability mass function Px (0) 12 Px(1) = %3D 12 3 Px(2) = %3D 12 4 Px(3) = 12 2 Px(4) = 12 1 Px(5) = %3D 12 He also knows that there is a profit of $1.00 on each cake that he sells and a loss (due to spoilage) of $0.30 on each cake that he does not sell. Assuming that each cake can be sold only on the day it is made, how many chocolate cakes should he bake to maximize his expected profit? Windows buiü I| ||
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