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 allhis 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?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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