1.) A rectangular microprocessor chip is designed to have an area of 81 mm^2. Wh

Question

1.) A rectangular microprocessor chip is designed to have an area of 81 mm^2. What must its demensions be if its perimeter is to be a minimum? Solve for the dimensions of this rectangle in mm? (Simplify your answer. Use a comma to separate answers as needed) 2.)Johnny is designing a rectangular poster to contain 18 in^2 of printing with a 1-in margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used? Solve for the dimensions of the poster than minimizes the amount of paper used in inches (Simplify your answer. Use a comma to separate answers)

Explanation / Answer

1.) let length be l and bredth be b so area = 81 = lb and perimeter is = P = 2(l+b) put l = 81/b from above equation we get P = 2(81/b + b) differentiate it wrt b we get P' = 2(1 -81/b^2) = 0 so b = 9 dimension = 9mm, 9mm 2.)Let inner dimension be again l and b to be painted so outer dimension will be l+4, b+2 amount of paper used = P = 2 (l+b) lb=18 so l = 18/b so P = 2(18/b +b ) differentiate it P' = 2(1-18/b^2) = 0 so b = 4.24 and l = 4.24 dimension = 8.24 , 6.24

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