According to u.s. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 108 inches, where by "girth" we mean the perimeter of the smallest end. what is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? such a package is shown below. assume y>x. what are the dimensions of the package of largest volume?

Answer:11,664 inches³Step-by-step explanation:Let 'S' be the length of the side of the square base and 'H' be height of the parcel.The U.S postal regulations specify that:[tex]4S +H = 108\\H=108-4S[/tex]The volume of the parcel is given by:[tex]V=H*S^2\\V=(108-4S)*S^2\\V=108S^2-4S^3[/tex]The value of 'S' for which the derivate of the volume function equals zero yields the maximum volume:[tex]\frac{dV(S)}{dS}= 216S-12S^2=0\\\frac{216S-12S^2}{S}=\frac{0}{S} \\216 - 12S =0\\S=18\ inches[/tex]Solving for 'H':[tex]H=108-4S = 108-(4*18)\\H= 36\ inches[/tex]The maximum volume is:[tex]V_{max} = 36*18^2\\V_{max} = 11,664\ inches^3[/tex]