SOLUTION: Thought I submitted this but not sure so trying again... Chemical Products makes two insect repellents, Regular and Super. The chemical used for Regular is 15% DEET, and the ch

Question 154127: Thought I submitted this but not sure so trying again...
Chemical Products makes two insect repellents, Regular and Super. The chemical used for Regular is 15% DEET, and the chemical used for Super is 25% DEET. Each carton of repellent contains 24 ounces of the chemical. In order to justify starting production, the company must produce at least 12,000 cartons of insect repellent, and it must produce at least twice as many cartons of Regular as of Super. Labor costs are $8 per carton for regular and $6 per carton for Super. How many cartons of each repellent should be produced to minimize labor costs if 59,400 ounces of DEET are available? I just need help setting up the problem, I think I can get the rest..
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The chemical used for Regular is 15% DEET, and the chemical used for Super is 25% DEET.
Each carton of repellent contains 24 ounces of the chemical.
In order to justify starting production, the company must produce at least 12,000 cartons of insect repellent, and it must produce at least twice as many cartons of Regular as of Super.
Labor costs are $8 per carton for regular and $6 per carton for Super.
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How many cartons of each repellent should be produced to minimize labor costs if 59,400 ounces of DEET are available? I just need help setting up the problem,
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Let R be # of Regular cartons; Let # of Super cartons be S.
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Each R carton contains 0.15*24 = 3.6 ounces of DEET
Each S carton contains 0.25*24 = 6 ounces of DEET
DEET INEQUALITY: 3.6R + 6S <= 59,400
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Quantity INEQUALITY: R + S >= 12000
Quantity INEQUALITY : R >= 2S
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Cost EQUALITY: Cost = 8R + 6S
Comment: This is the Objective equation you want to minimize.
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Cheers,
Stan H.

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