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    4 Stats Assignment

    Uploaded by

    Nadeem Kiani

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    4 Stats Assignment

    Uploaded by

    Nadeem Kiani
    3 views5 pages

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    © © All Rights Reserved

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    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    3 views5 pages

    4 Stats Assignment

    Uploaded by

    Nadeem Kiani

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 5

    Presented By:

    Alishba Imtaiz ( 006 )

    Awais Sohail (008)

    Raja Nadeem Asghar Kayani ( 032 )

    Presented To:
    Mam Sara Siddique

    Subject:
    Statistics

    Class:
    BBA 3 A
    SBE 13th Ed ( Anderson ), Chapter 6, Case Problem: Specialty Toys:

    Sol:
    1. Let X = the demand for the toy.

    X follows normal distribution with mean μ = 20000 and standard deviation σ.

    P (10000 < X < 30000) = 0.95

    P ((10000-20000)/σ < (X-20000)/σ < (30000-20000)/σ) = 0.95

    From tables of areas under the standard normal curve (30000-20000)/σ = 1.96

    σ = (30000-20000)/1.96 =10000/1.96 = 5102


    2. Probability of stock out with an order of K units is P(X > K) = P (Z > (K-20000)/5102),

    where Z is distributed as standard normal and z will be greater than K must be 1.000 –

    cumulative probability.

    Order (K) (K-20000)/5102 P(X > K): 1- cumulative


    probability

    15,000 -0.98001 0.836458876

    18,000 -0.392 0.652472052

    24,000 0.784006 0.216518215

    28,000 1.568013 0.058439102

    3. 15,000 units at a cost of $16/unit = $240,000 invested.


    a. Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000
    Profit: $25,000
    b. Most likely #sold: 15000 x 24 = $360,000 income
    Profit: $120,000
    c. Best case #sold: 15000 x 24 = $360,000 income
    Profit: $120,000
    18,000 units at a cost of $16/unit = $288,000 invested
    a. Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income

    Loss of -$23,000

    b. Most likely #sold: 18000 x 24 = $432,000 income

    Profit: $144,000

    c. Best case #sold: 18000 x 24 = $432,000 income


    Profit: $144,000
    24,000 units at a cost of $16/unit = $384,000 invested
    a. Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income

    Loss of $119,000

    b. Most likely #sold: 20000 x 24 + 4000 x 5 = $500,000 income

    Profit: $116,000

    c. Best case #sold: 24000 x 24 = $576,000 income

    Profit: $192,000

    Order Scenario 10000 Scenario 20000 Scenario 30000

    15000 8*10000-11*5000 8*15000=120000 8*15000 =


    =25000 120000
    18000 8*10000-11*8000 8*18000 = 144000 8*18000 =
    = -8000 144000
    24000 8*10000-11*14000 8*20000-11*4000 8*24000 =
    = -74000 =116000 192000
    28000 8*10000-11*18000 8*2000-11*8000 8*28000 =
    = -118000 =72000 224000

    Cost of sales per unit $24 - Cost of goods sold $16 = profit per unit 8

    Cost of sales per unit $24 – Cost of surplus inventory $5 – profit per $8 = coverage $11

    4. The order quantity to meet 70% demand is found by solving

    P(X < K) =0.70

    P (Z < (K-20000)/5102) = 0.70

    (K-20000)/5102 = 0.5244

    K = 20000 + 5102 * 0.5244 = 20000 + 2675 = 22,675 units to be ordered.


    5. The best case in which sales equals 30,000 units.

    Expected sales price = 22,675 * 24 = $544,200

    The suggested order quantities is 22,675, so the cost price is

    22,675*16 = $362,800

    Sales is expected to be 30,000 so there is no stock out and

    The projected profit = sales price – cost price

    544,200 – 362,800 = $181,400

    The most likely case in which sales equal 20,000 units

    Expected sale price = 544,200

    Cost is 22,675 * 16 = 362,800

    There is no stock out

    Projected profit = 544,200 – 362,800 = $181,400

    Worst case in which sales equal 10,000 units

    Sell for $24 based on cost of $16 per unit

    Expected sales = 10,000 * 24 = $240,000

    Cost price is 22,675 * 16 = $362,800

    Stock out is 22, 675 – 10,000 = 12,675 units.

    These will be sold at $5 per unit = 12,675 *5 = $63,375

    Total sale price = 240,000 + 63,375 = $303,375

    Projected profit = 362,800 – 303,375 = $59,425

    The best recommendation would be to order between 15,000 to 18,000 because even in the worst
    scenario, if the order quantity is 15,000 there will be profit of about $89,137.50 which puts you
    at the mid-range mark.

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