Question

1. A 7-11 convenience store orders identical bottles of wine from a wine distributor every week. Let X be the weekly demand from customers for this wine with the following probability distribution: X = x P(X=x) 0.1 0.2 0.4 0.1 It only costs the 7-11 store $60 to order each bottle of wine but the store charges $75 to customers per bottle. How many bottles of wine should the 7-11 store order each week to maximize its expected profit? [For this question, assume that the 7-11 store will always return all unsold wines back to the wine distributor for reimbursement at the end of the week. However, the reimbursement is only half the cost (i.e., only $30, not $60).] [Total: 15 marks

Answer 1

o As we are given, x: The weekly demand forom customers for this wine with me with the following probability distribution, P (X=%) 0.4 0.2 0.2 er Dw New 0.4 0.1

Page 2 As per the given question, I have to maximize profit, and how many bottles should be ordered? But Here, we are given the Information on demand, so, I will calculate the Expected Demand, or that is E (2), = 3x. Plx=3) Because Wine should be ordered as per the demand- So, E(X)= 1x0.1 + 2 *0.2+ 3×0.27 0.4x4 + 500.4 1.6 0.1 +0.4+ 0.6+ 1.6+ 0.5. 3.2 L = 3 (-). store ar are So, the wine should order 3 battles he can order 4 bottles as there e return value / reimbursement.

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