A beverage can manufacturer makes three sizes of soft drink cans-Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 90 production hours per day, and the daily supply of metal, no more than 120 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans for each size.
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Cans
Large
Medium
Small
Maximum
Metal (kg)/batch9
6
5
120
Machines' Time (hr)/batch4.4
4.2
4
90
Profit/batch$50
$45
$42
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Develop a linear programming model to maximize profit and determine how many batches of each can size should be produced.
What will be an ideal response?
M = number of batches of Medium cans produced
S = number of batches of Small cans produced
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Max 50
L + 45 M + 42 S
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s.t.
9L + 6M + 5S ? 120
4.4L + 4.2M + 4S ? 90
L, M, S? 0
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