1) Maile’s Flower Shop gets a rose delivery once per week for which they pay 79
ID: 376563 • Letter: 1
Question
1) Maile’s Flower Shop gets a rose delivery once per week for which they pay 79 cents per rose. Roses are sold for $1.32 per bud. At the end of the week, Maile sells all remaining roses to a potpouri maker for 6 cents apiece. Sales are normally distributed with a mean of 1,399 roses per week and a standard deviation of 55. How many roses should Maile purchase?
2)
The Kaneohe Trading Company makes a fastener that they use in another process. The firm operates 264 days per year and uses the fasteners at a fairly steady rate of 230 per day. Fasteners can be produced at a rate of 710 per day. Annual storage costs is $3.50 per fastener and setup cost to produce more fasteners is $90.
What is the cycle time in days?
Your Answer:
Explanation / Answer
Answer to Q.1:
Purchase price for Maile’s flower shop = C = 79 cents per rose
Selling price by Maile’s flower shop = P = 132 cents per rose
Salvage price for Maile by selling to Potpuri maker = S = 6 cents
Thus ,
Underage cost = Cu = 132 – 79 = 53 cents
Overage cost = Co = 79 – 6 = 73 cents
Hence,
Critical ratio = Cu/ ( Cu + Co) = 53/ ( 53 + 73 ) = 53/126 = 0.4206
0.4206 is the probability of the optimum quantity which should be ordered
Corresponding Z value for probability 0.4206 = - 0.20
Hence, number of roses should Maile purchase = Mean value of sales + Z x Standard deviation value of sales = 1399 – 0.2 x 55= 1399-11=1388
MAILE SHOULD PURCHASE 1388 ROSES
Answer to Q.2:
This will be solved using Economic Production Quantity ( EPQ ) model.
EPQ = Square root ( 2 x Cs x D / Ch x ( 1 – d/p) )
Where ,
D = Annual demand = 230/ day x 264 days = 60720
Ch = Annual unit storage cost = $ 3.5
Cs = annual unit set up cost = $90
Daily demand of fasteners = d = 230 per day
Daily production rate = p = 710 per day
Hence , EPQ = Square root ( 2 x 90 x 60720 / 3.5 x ( 1 – 230/710) ) = Square root ( 10929600 / 3.5 x 0.676) = 2149.28 ( 2149 rounded to nearest whole number )
Hence cycle time = EPQ/ Daily production capacity = 2149/710 = 3.026
CYCLE TIME = 3.026
MAILE SHOULD PURCHASE 1388 ROSES
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