C&A Candy produces two kinds of gumdrops: regular and sugar-free.The data on the
ID: 350804 • Letter: C
Question
C&A Candy produces two kinds of gumdrops: regular and sugar-free.The data on these gumdrops are given below:
Regular
Sugar-Free
Demand (lbs per hour)
30
10
Changeover time (min)
60
30
Production rate (lbs per hour)
80
80
How many lbs of gumdrops should C&A produce in each production cycle to minimize inventory while satisfying demand?
O 30
O 80
O 90
O 120
Please be as detailed as possible in your response. I want to be able to understand the process. Thank you very much in advance!
Regular
Sugar-Free
Demand (lbs per hour)
30
10
Changeover time (min)
60
30
Production rate (lbs per hour)
80
80
Explanation / Answer
Puting it very simply, take the stages of a production cycle sequentially. Let that the company first does set up for 'Regular' and then produces it with a batch size of 'B1'. Then it does set up for the 'Sugar-Free' and then produces that with a batch size of 'B2'.
So, how much time has passed?
1 hour (for setting up for Regular) + B1/80 (for producing Regular) + 0.5 hours (for setting up for Sugar-free) + B2/80 (for producing Sugar-free) = 1.5 + (B1+B2)/80 hours
What was the demand during these hours?
30 x {1.5 + (B1+B2)/80} for the Regulars
10 x {1.5 + (B1+B2)/80} for the Sugar-free
We don't want to gather inventory so the production and demand should match i.e.
30 x {1.5 + (B1+B2)/80} = B1
10 x {1.5 + (B1+B2)/80} = B2
Little simplification will give us,
45 + (3/8) (B1+B2) = B1
15 + (1/8) (B1+B2) = B2
Addting both sides, 60 + (4/8) (B1+B2) = (B1+B2) or, B1+B2 = 120. So, 120 lbs of gumdrops should C&A produce in each production cycle to minimize inventory while satisfying demand.
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