Question

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 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?

Answer 1

Answer:

Answer is 20.567 %

Step-by-step explanation:

First subtract 2,250 by 1.50 +

Answer 2

He should choose 20.567 % in order to maximize his expected profit in the long run.

Given,

The operating cost for the boat is = $2,250 each day.

The price per pound that the restaurant is willing to pay follows a triangular distribution with,

Minimum value = $1.50

Maximum value = $5.50

Likeliest value = $3.50.

Now, 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 above mentioned conditions.

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 √12,500 pounds.

So, he should choose 20.567 % in order to maximize his expected profit in the long run.