Amir operates a large lobster boat. The operating cost for the boat is $2,250 each day. At the end of each day, he sells all his freshly caught lobster to either the local restaurant or the local grocery store with the following conditions: • The price per pound that the restaurant is willing to pay follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50. • The price per pound that the grocery store is willing to pay is decreasing with more lobsters: $3.85 - $0.0005 * y, where y is the total lobster amount sold in pounds. • The amount of lobster that Amir catches in a single day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds. Amir decides to sell a fixed percentage of lohster to the local restaurant and the rest to local grocery
Amir operates a large lobster boat. The operating cost for the boat is $2,250 each day. At the end of each day, he sells all his freshly caught lobster to either the local restaurant or the local grocery store with the following conditions: • The price per pound that the restaurant is willing to pay follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50. • The price per pound that the grocery store is willing to pay is decreasing with more lobsters: $3.85 - $0.0005 * y, where y is the total lobster amount sold in pounds. • The amount of lobster that Amir catches in a single day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds. Amir decides to sell a fixed percentage of lohster to the local restaurant and the rest to local grocery
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:Amir operates a large lobster boat. The operating cost for the boat is $2,250 each day. At the end of
each day, he sells all his freshly caught lobster to either the local restaurant or the local grocery
store with the following conditions:
• The price per pound that the restaurant is willing to pay follows a triangular distribution with
minimum value $1.50, maximum value $5.50, and likeliest value $3.50.
The price per pound that the grocery store is willing to pay is decreasing with more lobsters:
$3.85 - S0.0005 * y, where y is the total lobster amount sold in pounds.
• The amount of lobster that Amir catches in a single day follows a normal distribution with
mean 1,500 pounds and standard deviation sqrt(12,500) pounds.
Amir decides to sell a fixed percentage of lobster to the local restaurant and the rest to local grocery
stores. Using either math or simulation, can you help Amir determine what percentage he should
choose in order to maximize his expected profit in the long run?
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