A factory produces 30,000 cell phones per day. The dimensions of the cell phone
ID: 354589 • Letter: A
Question
A factory produces 30,000 cell phones per day. The dimensions of the cell phone box are 4x3x1.5 inches. Each box weighs 6 ounces. We wish to have space for a 4 day supply of phones. The phone boxes are to be packed in a larger carton, which must be transportable manually. The cartons are to be stacked on each other on the floor such that the workers can access them without additional equipment. How much floor space will you need? (Also specify the carton dimensions)
you can make any assumptions regarding maximum weight/dimensions
Explanation / Answer
Part I
Total boxes to be stored=per day production * no of days of production
=30000*4=120000 boxes
Assuming a carton can be picked manually from the height of 5 ft. ie height cannot be more than 5 feet, if the carton has to be picked manually
Based on 1.5 inch box height, max boxes which can be stacked above each other are =5*12/1.5=40 boxes
Therefore
No of boxes stacked in height=40
No of boxes stacked width wise=y
No of boxes stacked length wise=x
Total no of boxes=40*x*y=120000
Or x*y=30000
Floor area=total width*total length=(3*x)*(4*y)=12*xy or 12*30000 sq inches or 30000 sq feet
Assuming 10% extra floor area for material and man movement total area required = 30000*1.1 = 33000 Sq feet
Part II
Assuming Max weight which a person can lift=60 pounds
Therefore assuming max weight of carton=60 pounds
Weight of each box=1 pound
Max boxes per carton=60/1=60 boxes
Considering 5 boxes in height and 8 boxes stacked above, within a carton
No of boxes stacked in height=5
No of boxes stacked in Length=a
No of boxes stacked in width=b
Or 60=5*a*b
Or a*b=12
Possible solutions 4,3 and 6,2
So the carton dimensions should be 5,4,3 inches
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