a delivery company accepts rectangular boxes the sum of whose length and girth (perimeter of a cross-section) does not exceed 108 in. find the dimensions of an acceptable boc
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The dimensions of an acceptable box is 18 x 36 inches.If the package has a combined length and girth of 108 inches. We can determine that:4x + y = 108We are also assuming that the cross section is square, so:V = x²yLet’s solve for y in the first equation and plug it in to the second equation:y = 108- 4xV = x²(108- 4x)V = 108x² – 4x³In order to solve for the maximum is when V’ = 0V’ =216x – 12x² = 0x(216- 12x) = 0Therefore, we have 2 solutions,x = 0216- 12x = 012x = 216x = 18x = 0 is when the package is a minimum, so the maximum occurs when x = 18. Now let’s solve for yy = 108- 4x = 108- 4(18) = 36The answers are:x = 18 inchesy = 36 inchesTherefore, the dimensions of an acceptable box is 18 x 36 inches.To learn more about perimeter refer herehttps://brainly.com/question/24571594#SPJ4