Question

Problem 3-07 (Algorithmic) The demand for Carolina Industries’ product varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company’s monthly demand: Unit Demand Probability 100 0.15 200 0.2 300 0.35 500 0.3 (a) If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product? Monthly order quantity = units (b) Assume that each unit demanded generates $50 in revenue and that each unit ordered costs $40. How much will the company gain or lose in a month if it places an order based on your answer to part (a) and the actual demand for the item is 225 units? For subtractive or negative number use a minus sign. (Example: -300) $ (c) What are the variance and standard deviation for the number of units demanded? If required, round your answers to two decimal places. Variance = Standard deviation =

Answer 1

a) Expected value of demand=Di*Pi ; where i=1,2,3,4 for demand =100,200,300,500 respectively

Expected value of demand=100*0.15+200*0.2+300*0.35+500*0.3= 310 units

b)Revenue per unit =50

Cost per unit =40

Actual demand=225

Net profit =Total sales-Total costs

=Actual demand*revenue per unit -Expected demand*cost per unit

=225*50-310*40

=-1150 (loss)

The company will incur a loss of $ 1150 per month

c.Variance of number of units demanded =VAR(B2:E2)=29166.67

Standard deviation of number of units demanded=STDEV(B2:E2)=170.78