The cost C of manufacturing a certain product can be estimated by the formula C = 0.03rst^2, 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%, s is increased by 20%, and t is decreased by 30%, 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
E. 24% decrease
OA is D
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If C is the cost of manufacturing a product that requires r & s pounds & time t, then logically if the amounts increase & the time for manufacturing them reduces, the cost for manufacturing them decreases, because it takes less time to produce more amounts. So, we are left with options D & E.
if r=8 pounds, s=10 pounds & t=10hrs, then the estimated cost as per the formula is: C = 0.03*8*10*100 ==> 3*8*10=240
now, if r increases 50%, then r=12. If s increases 20%, then s=12 & if t decreases 30%, then t=7. So,
C = 0.03*12*12*49 ==> 3/100*12*12*50~ ==> ~216
So, the decrease is 24/240 = ~10% (since we rounded off 49 to 50).
if r=8 pounds, s=10 pounds & t=10hrs, then the estimated cost as per the formula is: C = 0.03*8*10*100 ==> 3*8*10=240
now, if r increases 50%, then r=12. If s increases 20%, then s=12 & if t decreases 30%, then t=7. So,
C = 0.03*12*12*49 ==> 3/100*12*12*50~ ==> ~216
So, the decrease is 24/240 = ~10% (since we rounded off 49 to 50).