Section

Lagrange polynomials of the optimized redesigned bottle

S1

$P_1\left(x\right)=1.1$

S2

$P_2\left(x\right)=0.0034921x^5-0.040476x^4+0.21706x^3-1.3089x^2+5.7384x-5.1167$

S3

$\begin{array}{c}{P}_3\left(x\right)=-0.036829113x^6+1.4915791x^5-24.923167x^4+219.65835x^3\\ -1075.681x^2+2772.3003x-2931.6348\end{array}$

S4

$P_0\left(x\right)=4.4$

S5

$P_4\left(x\right)=-0.0406912x^3+0.99403x^2-7.40008x+19.7863$