Question

AP Calculus
You are desigining a rectangular poster to contain 256 in^2 of printing with 3 in. margin at the top and bottom and a 2-in. margin at each side. What is the overall dimensions will minimize the amount of paper used?(round to the nearest whole number)
A. 13 in by 20 in
B. 15 in by 23 in
C. 17 in by 26 in
D. 19 in by 23 in
E. 20 in by 22 in
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Answer 1

Here's our figurewe are given that the printed area is the printed area will be\[P=xy=256\]and the whole area will be\[A=(x+4)(y+6)\]after we include the margins.
Solve the first equation for either x or y so we can get the second equation in terms of one variable\[P=xy=256\to y=\frac{256}{x}\]theh sub this into the second equation\[A=(x+4)(y+6)\to A(x)=(x+4)(\frac{256}{x}+6)\]and we can find maximums and minimums of this function by setting\[\frac{dA}{dx}=0\]so find the derivative of the function above (in terms of x) and set it to zero.
Then just make sure that the number you found is a minimum, not a max.