A poster is to have an area of 180 in2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. Find the exact dimensions that will give the largest printed area.
Accepted Solution
A:
Answer:x = 2√30y= 3√30Step-by-step explanation:Area= 180in^2For the larger shape,Let the length be x and the width be yA = x. yx. y = =180y= 180/xFor the smaller shape, lenght= x-2 while width = y-3Area = (x-2)(y-3) A(x) = (x-2)(y-3)Put y= 180/x into A(x)= (x-2)(180/x -3)= 180 - 3x - 360/x + 6Differentiate A(x) with respect to xA'(x) = -3x+ 360/x^2A'(x) = 00 = -3x + 360/x^23x = 360/x^23x^3 = 360x^3 = 360/3x^3 = 120x = cuberoot 120x = 2√30Recall that y= 180/xy = 180/2√30y= 90/√30By rationalizing the surd, we have y = 90/√30 * √30/√30y = (90√30) /30y = 3√30x = 2√30, y = 3√30