Question $4$

A coffee shop needs to stock a certain amount of coffee beans to keep up with demands. The coffee shop

earns a profit of $"a"$ dollars for every ton of beans sold. However, due to the perishable nature of coffee

beans, any unsold stock incurs a loss of $"$b$"$ dollars per ton, as the beans lose their freshness and have to

be disposed of$.$ The demand for the coffee beans, measured in tons, is a random variable $Y$ that follows

an exponential distribution with parameter $.$ What is the optimal amount of coffee beans to stock in

order to maximize the expected profit?