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minimize labor costs?
Chemical Products makes two insect repellants, Regular and Super. The chemical used for Regular is 15% DEET, and the chemical used for Super is 25% DEET. Each carton of repellant contains 22 ounces of the chemical. In order to justify starting production, the company must produce at least 10,200 cartons of insect repellant, 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 repellant should be produced to minimize labor costs if 54,450 ounces of DEET are available?
Note: It would be helpful if you can provide how to get the solutions. Thanks!
1 Answer
- 7 years agoFavorite Answer
If this is a management science question, you would set it up like this:
Min 8R + 6S (This is the cost function you want to
minimize)
s.t.
S + R >= 10,200 (Production constraint)
-2S + R >= 0 (This is the constraint that says there must
be
at least two times as many cartons of
regular
as of super. This is just the simplified
version
of R=2S.)
5.5S + 3.3R <= 54,450 (Last constraint has to do with the amount of
DEET in each carton. 15% of 22 oz is 3.3 oz
and 25% of 22 oz. is 5.5 oz.
If you're not in a Management Science course, you could graph all the lines and find the optimal solution the hard way, or you could plug the constraints in to management science software such as QM for Windows. That's how I arrived at the solution of R=6800 and S=3400. Plugging those in gives you a cost of $74,800.
