SA=2H(L+W)+LW for open box 20=2H(4+W)+4(W) distribute 20=8H+2WH+4W divide both sides by 2 10=4H+WH+2W solve for 1 variable, pick W 10-4H=WH+2W 10-4H=W(H+2) (10-4H)/(H+2)=W
V=LWH subsitute 4 for V, subsitute H for H and (10-4H)/(H+2) for W V=(4)(H)(10-4H)/(H+2) V=(40H-16H²)/(H+2) find max value take deritivitive of this thing V'=-16(H²+4H-5)/((H+2)²) using sign chart sign changes from positive to negative at H=1
so at H=1 find W
W=(10-4H)/(H+2) W=2
the dimeionts are
length=4ft width=2ft height=1ft (the volume is 8 cubic feet)