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Optimization Problem:
Ronnie is designing a poster to contain 50in^2 of printing with margins of 4 inches each at the top and at the bottom and margins of 2 inches at each side. What overall dimensions will minimize the amount of paper used?
 one year ago
 one year ago
Optimization Problem: Ronnie is designing a poster to contain 50in^2 of printing with margins of 4 inches each at the top and at the bottom and margins of 2 inches at each side. What overall dimensions will minimize the amount of paper used?
 one year ago
 one year ago

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kropot72Best ResponseYou've already chosen the best response.1
Let printing width = w and let printing length = x x * w = 50 w = 50/x Overall area A = (w + 4)(x + 8) Sustituting for w gives: A = (50/x + 4)(x + 8) Multiplying out gives: A = 4x + 400/x + 82 We need to find the value of x that makes A a minimum. Are you following so far?
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
wait, are you sure you got the multiplication right for A? i got something else
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
just kidding, i did somethign wrong here
 one year ago

kropot72Best ResponseYou've already chosen the best response.1
Gr8. To find the value of x to give the minimum value of A we differentiate A with respect to x: dA/dx = 4  400/x^2 Now put the result equal to zero and solve for x: 4  400/x^2 = 0 x^2 = 400/4 = 100 \[x=\sqrt{100}=10\]
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
that is the correct answer, thank you sir
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
my problem is i can't figure out the relevant equation to derive etc.
 one year ago

kropot72Best ResponseYou've already chosen the best response.1
So the optimum printing length is 10 inches. The optimum printing width is found from: x * w = 50 10 * w = 50 w = 5 So the optimum overall dimensions will be: Length = (10 + 8) = 18 inches Width = (5 + 4) = 9 inches
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
could you do another one for me? or just part of it, i have it figured out but the arithmetic was crazy, i had to use wolfram, maybe there was another simpler way?
 one year ago

kropot72Best ResponseYou've already chosen the best response.1
Do you follow the method to get the overall dimensions?
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
actually it's just 5" x 10"
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
we included the area of the print in the overall dimensions
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
A = (w + 4)((50/w) + 8) that's print area + margins = overall area
 one year ago

kropot72Best ResponseYou've already chosen the best response.1
Sorry for error. You are right. Good work :)
 one year ago
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