Question

In a store, the daily demand for milk (in litres) is a random variable having Exp(λ) distribution, where λ > 0. At the beginning of the day, the store purchases c (> 0) litres of milk at a fixed price b (> 0) per litre. The milk is then sold to the customers at a fixed price s (> b) per litre. At the end of the day, the unsold milk is discarded. Then the value of c that maximizes the expected net profit for the store equals

• A. $-\frac{1}{λ}\ln(\frac{b}{s})$
• B. $-\frac{1}{λ}\ln(\frac{b}{s+b})$
• C. $-\frac{1}{λ}\ln(\frac{s-b}{s})$
• D. $-\frac{1}{λ}\ln(\frac{s}{s+b})$

Answer 1

Answer: (A)

$-\frac{1}{λ}\ln(\frac{b}{s})$

Answer 2

The correct option is (A) : $-\frac{1}{λ}\ln(\frac{b}{s})$.