You are designing a rectangular poster to contain 50 in^2 of printing with a 4 in. margin at the top and bottom and a 2 inch margin at each side. what overall dimensions will minimize the amount of paper used?

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 printed area = 50 = xy 
paper size, P(x) 
= (x + 2*2)(y + 2*4) 
=(x + 4)(y + 8) 
= xy + 4y + 8x + 32 
= 8x + 4(50/x) + (50 + 32) 
= 8x + 200/x + 82 

P'(x) = 8 - 200/x^2 = 0 
x = √(200/8) = 5 (for x > 0) 

paper dimension = 9 x 18