Question
Suppose that the daily demand (π·) for a certain item in the capital market is random and behaves according to a uniform probability (quantity) law with π = 0.1, β¦ ,19. Every day, π₯ units of the item are brought for sale, which are sold at 5 mu per unit and, if not sold, 2 mu are lost (for storage, return or other). Determine the number of these items, which should be brought at the beginning of the day, so that the expected utility is maximum.
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Answer to a math question Suppose that the daily demand (π·) for a certain item in the capital market is random and behaves according to a uniform probability (quantity) law with π = 0.1, β¦ ,19. Every day, π₯ units of the item are brought for sale, which are sold at 5 mu per unit and, if not sold, 2 mu are lost (for storage, return or other). Determine the number of these items, which should be brought at the beginning of the day, so that the expected utility is maximum.
Murray
4.592 Answers
Since there's a uniform distribution, we consider the two cases where the profit equations exist:
1. **Demand
2. **Demand
Integrate over both segments accordingly:
Solve these integrals:
Evaluating these:
1. First part:
2. Second part:
Combine and simplify:
After simplifying, the expected profit equation in terms of
Set the derivative of accumulated profit with respect to
Therefore:
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