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# The cost C of manufacturing a product can be estimated by the formula

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The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 02:32
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65% (hard)

Question Stats:

61% (03:53) correct 39% (03:15) wrong based on 31 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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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 04:30
1
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Let r=s=t=100

C = 0.03*r*s(t^2)
=0.03*100*100*(100^2)
=3,000,000

r1 = 50% more than r = 150
s1 = 20% more than s =120
t1 = 30% less than t = 70

C1= 0.03 * 150 *120 * 70 * 70
=0.03 * 1800 * 4900
= 54*4900
=264600

Decrease = C-C1 = 3,000,000-264600=35400
%Decrease = 35400/300000 * 100 = 354/30 = 11.8 ~ 12% Decrease

OA D
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 05:15
tracyyahoo wrote:
The cost C of manufacturing a certain product can be estimated by the formular C=0.03rs(t^2), where r and s are the amounts, in pounds, oof the two major ingredients and t is the production time in hours. If r is increased by 50%, s is increased by 20%, and t is decreased by 30%, by approximately what percent will the estimated cost manufacturing the product change?

a) 40% increase
b) 12% increase
c) 4% incease
d) 12% decease
e) 24% decrease

pls explain me, thank you. I need it.

From the formula we deduce that C directly proportional to r, s and t^2
hence an increase or decrease in these values will directly change the value of C by that factor

There new r => 1.5r
new s => 1.2s
new t^2 = (0.7t)^2 = .49t^2
let the constant 0.03 be termed as A

Putting these new values: C1 = A*1.5r*1.2s*.49t^2
C1 = 0.882A*r*s*t^2 = 0.882(C)

There the net value decrease by 12% approx

Hence D
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 12:25
Hi

How did you guys determine if it was an increase or decrease?

is it because the value of c > c1?
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 14:19
Sudhanshuacharya wrote:
tracyyahoo wrote:
The cost C of manufacturing a certain product can be estimated by the formular C=0.03rs(t^2), where r and s are the amounts, in pounds, oof the two major ingredients and t is the production time in hours. If r is increased by 50%, s is increased by 20%, and t is decreased by 30%, by approximately what percent will the estimated cost manufacturing the product change?

a) 40% increase
b) 12% increase
c) 4% incease
d) 12% decease
e) 24% decrease

pls explain me, thank you. I need it.

From the formula we deduce that C directly proportional to r, s and t^2
hence an increase or decrease in these values will directly change the value of C by that factor

There new r => 1.5r
new s => 1.2s
new t^2 = (0.7t)^2 = .49t^2
let the constant 0.03 be termed as A

Putting these new values: C1 = A*1.5r*1.2s*.49t^2
C1 = 0.882A*r*s*t^2 = 0.882(C)

There the net value decrease by 12% approx

Hence D

I am using the same approach as above:

50% increase = 1.5r
20% incease = 1.2s
30% decrease = .7r

So new value = (1.5r)(1.2s)(.7r)^2=(15/10*12/10*49/100)(.03rst^2)
Old value = (.03rst^2)

Now I am approx. 49 to 50 for faster calculation -
New value = (15/10*12/10*50/100) = 180/100*1/2=(90/100)(.03rst^2)

New value is 90% of the old value
So 10% less ....Let me see any value near 10% decreases
B is the closest...So I go with B
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 14:21
arjun007 wrote:
Hi

How did you guys determine if it was an increase or decrease?

is it because the value of c > c1?

Hope it is clear to you how it is decreasing ... Taking a larger value like - 50 even decreased,so obviously a smaller value - 49 will always decrease
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 14:24
The reason for approximating is sometimes we make silly mistakes in calculation.
So the best way is to pick smart numbers when needed.........Again it is up to you to decide the approach that works nest for you.....
Some people can calculate this in head in (5-10) secs....then do not approximate...This is for the other folks who spend 20-30 secs on multiplication(calculation)
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 17:22
Thank you so much you guys, Why I haven't thought about using Plug-in strategy.

This question is very simple after I saw your explanation. Thank you again for the effot.

Let r=s=t=100

C = 0.03*r*s(t^2)
=0.03*100*100*(100^2)
=3,000,000

r1 = 50% more than r = 150
s1 = 20% more than s =120
t1 = 30% less than t = 70

C1= 0.03 * 150 *120 * 70 * 70
=0.03 * 1800 * 4900
= 54*4900
=264600

Decrease = C-C1 = 3,000,000-264600=35400
%Decrease = 35400/300000 * 100 = 354/30 = 11.8 ~ 12% Decrease

OA D
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  31 Jul 2011, 18:14
tracyyahoo - Give kudos to jamifahad if you liked his approach...

That is one way of saying thanks for the person spending time on your questions.....
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  01 Aug 2011, 17:04
C = 0.03 r s t^2
New C = C1 = $$0.03(150/100)r(120/100)s((70/100)^2)t^2$$

=(882/1000)[0.03rst^2]
as C>C1 => its a decrease

% decrease = ((original - new) /original)*100

= (118/1000) *100
~= 12%

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The cost C of manufacturing a product can be estimated by [#permalink]  05 Oct 2012, 07:03
1
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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
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Last edited by Bunuel on 05 Oct 2012, 07:11, edited 1 time in total.
Renamed the topic.
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Re: The cost C of manufacturing a product can be estimated by [#permalink]  02 May 2013, 21:22
2
KUDOS
Initial Cost C = 0.03rs$$t^2$$.

Changed Cost = $$0.03 * 1.5r * 1.2s *$$ $$(.7t)^2$$
= $$0.03 * .882 * rs$$$$t^2$$
= .882 C
Change in cost = $$(.882 - 1) * 100$$
= - 11.8%
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]  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]  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]  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)
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]  19 Dec 2014, 13:09
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Re: The cost C of manufacturing a product can be estimated by the formula   [#permalink] 19 Dec 2014, 13:09
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