Demand (in units) Probability 300 0.20 400 0.30 500 0.35 600 0.15 (a) If the com
ID: 2916060 • Letter: D
Question
Demand (in units)
Probability
300
0.20
400
0.30
500
0.35
600
0.15
(a) If the company orders the expected monthlydemand amount, what should ABC’s monthly order quantity befor this product?
(b) Assume that ABC company orders the amount in (a),what is the probability that the company has the stock-out problem?(Note: (i) stock-out problem means that the demand is greater thanthe on-hand stock for the month; (ii) we assume that the companycan only order once at the beginning of the month.)
(c) Compute the standard deviation of the monthlydemand?
(d) Assume that each unit sold generates $70 in revenueand that each unit ordered cost $50. If the monthly order quantityis chosen to be 500 units, what is the expected monthly profit?(note: Profit=Revenue – Cost)
Demand (in units)
Probability
300
0.20
400
0.30
500
0.35
600
0.15
Explanation / Answer
a) The expected monthly demand is 300*0.2 + 400*0.3 + 500*0.35 +600*0.15 = 445 b) The probability of having a stock-out problem occurs when thedemand is 500 or 600, that is 0.35 + 0.15 = 0.5 c) The variance is calculated as follows: (300-445)^2*0.2 + (400-445)^2*0.3 + (500-445)^2*0.35 +(600-445)^2*0.15 = 9475 The standard deviation is sqrt(9475) = 97.34 d) The expected monthly profit is 445*70 - 500*50 = 6150. Since theexpected number sold is a random variable while the number orderedis chosen to be 500.
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