Problem 1 [5 marks]. The demand for produce B in hundreds of pounds can be model

Question

Problem 1 [5 marks]. The demand for produce B in hundreds of pounds can be modeled approximately by the following probability density function: 6 The owner of a local produce store would like to find the optimal quantity to order to maximize her expected profit. It costs her $0.09/lb to purchase and stock the produce, after which she can sell for $0.13/lb. She plans to purchase 100k (for some unknown k) pounds of produce. Find the gptimal supply she should have on hand, and the corresponding expected profit.

Explanation / Answer

optimal quantity can be found by equating first derivative of probability density function with zero.

Therefore after solving we get b = 1.5.

So the optimal supply she should have on hand is 150 pounds and the corresponding expected profit is 6 dollars.

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