SOLUTION: The cost C of manufacturing a certain product can be estimated by the formula C = 0.03rst2, where r and s are the amounts, in pounds, of the two major ingredients and t is the prod

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Question 3655: The cost C of manufacturing a certain product can be estimated by the formula C = 0.03rst2, where r and s are the amounts, in pounds, of the two major ingredients and t is the production time in hours. If r is increased by 50 percent, s is increased by 20 percent, and t is decreased by 30 percent, by approximately what percent will the estimated cost of manufacturing the product change?
(A) 40% increase
(B) 12% increase
(C) 4% increase
(D) 12% decrease
Answer by Zenock(15) About Me  (Show Source):
You can put this solution on YOUR website!
For the question as written none of the answers are correct. Therefore I believe the original formula should have read...
C=0.03rst%5E2
Assuming this is correct.
Lets let d=the percentage of change in cost...
Then:C%2Bd%2AC=C%281%2Bd%29=0.03%28r%2B.5r%29%28s%2B.2s%29%28t-.3t%29%5E2=0.03%281.5r%29%281.2s%29%28.7t%29%5E2=0.03%2A0.882%28rst%5E2%29
C=0.03rst%5E2 so %281%2Bd%29%280.03rst%5E2%29=0.03%2A0.882%28rst%5E2%29
So: 1%2Bd=0.882 so d=-0.118 which is approximately -12%.
The answer is (D) 12% decrease