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The cost C of manufacturing a product can be estimated by

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The cost C of manufacturing a product can be estimated by [#permalink] New post 05 Oct 2012, 07:03
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72% (02:46) correct 28% (02:21) wrong based on 75 sessions
The cost C of manufacturing a product can be estimated by the formula C= 0.03 rs t^2, where r ans s are amounts, in pounds, of two major ingredients and t is production time in hours. if r is increased by 50%, s increased by 20% and t decreased by 30%, by approximately what % will the estimated cost of manufacturing the product change.

A. 40% increase
B. 12% increase
C. 4% increase
D. 12% decrease
E. 24% decrease
[Reveal] Spoiler: OA

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Last edited by Bunuel on 05 Oct 2012, 07:11, edited 1 time in total.
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Re: The cost C of manufacturing a product can be estimated by [#permalink] New post 02 May 2013, 21:22
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Initial Cost C = 0.03rst^2.

Changed Cost = 0.03 * 1.5r * 1.2s * (.7t)^2
= 0.03 * .882 * rst^2
= .882 C
Change in cost = (.882 - 1) * 100
= - 11.8%
Negative sign indicates a decrease.
So.it's a 12% decrease.

Ans : option D.
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Last edited by subhendu009 on 03 May 2013, 10:19, edited 1 time in total.
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Re: The cost C of manufacturing a product can be estimated by [#permalink] New post 02 May 2013, 21:46
[(1.5)*(1.2)*(0.7)*(0.7) - 1]*100% = [1.8*0.49 - 1]*100% = - 12%
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Re: The cost C of manufacturing a product can be estimated by [#permalink] New post 02 May 2013, 22:09
Expert's post
lets initial values be as follows
r=10, s=10, t=10

Initial cost = \frac{3}{100} X 10 X 10 X 100

Initial Cost = 300

Revised values will be

r=15 -----------------> increase of 50%

s=12 -----------------> increase of 20%

t=7 -------------------> decrease of 30%

Revised cost = \frac{3}{100} X 15 X 12 X 49

Revised cost = 265 approximatly

Reduction of 35 approx

reduction of 12% approx
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Re: The cost C of manufacturing a product can be estimated by [#permalink] New post 05 Feb 2014, 03:35
50 % Increase = 1.5r
20 % increase = 1.2 s
30 % decrease = 0.7t --> Formula says we have t² hence 0.7²

multiply: 1.5*1.2*0.7² = 0.882 = 12 % decrease. (1-0.882)
Re: The cost C of manufacturing a product can be estimated by   [#permalink] 05 Feb 2014, 03:35
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