04.7.B.Optimization2: Problem 3 Previous Problem Problem List Next Problem (1 po

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04.7.B.Optimization2: Problem 3 Previous Problem Problem List Next Problem (1 point) A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides as in the figure below Suppose that the box height is h 3:n and that t is constructed using 106 in 2 of cardboard (.e AB- 106 which values A and B maximize the volume? in in Note: You can earn partial credit on this problem. Preview My Answer Submit Answers You have attempted this problem 0 times You have T attempts remaining Email instructor Pagè generated at Ofi/01/2018?08:30pm, El 996-2 theme matn4 1 Pa-2 13 The WeBWork

Explanation / Answer

Volume = h(A-2h)(B-2h)

V = 3(A-2h)( 106/A - 2h) = 3(A-6)(106/A - 6) = -18A - (1908/A) +426

V ' = -18 +(1908/A2)

V ' =0

-18 +(1908/A2)=0

A2 = 1908/18

A =sqrt 106 = 10.3 in

B = 106/ 10.3 = 10.3 in

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