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Calculus/applications of absolute extrema

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Expert: Alon Mandes - 1/17/2010


Question
good day, sir!

i'm doing some practice problems for my calculus exam, and i saw this question:

A cardboard poster containing 32 in.^2 of printed region is to have a margin of 2in. at the top and bottom and 4/3 in. at the sides. Determine the dimensions of the smallest piece of cardboard that can be used to make the poster.

i looked at the answer key to check my answer but my answer is different to the supposedly correct answer. i think i made the right calculations but..


thanks for your help.

Answer
If we set the dimensions of the cardboard as : AxB , then
The area of the printed region is : S=[A- 8/3][B-4] . Where AB=32 --> B=32/A . Thus,
S=[A- 8/3][32/A -4] . To find minimum, we derive S with respect of A, & solve S'=0 :
S'=[32/A -4]-(32/A^2)[A- 8/3]
S'=0 --> 32/A - 4 - 32/A + 85.33/A^2 =0
32A-4A^2-32A+85.33=0
4A^2=85.33
A^2=21.33
A=4.61
Let's find B : B=32/A = 32/4.61=6.94
The Dimensions are : 4.61 X 6.94

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

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M.A in Mathematics & Bs.c in Electronics.

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