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Correct Answer : A

The shelf life is about 121 days.

Oxygen passes through the two layers in series, so their resistances \(L/P\) add:

\[ \begin{aligned} R_{LDPE} &= \frac{0.15}{4.18 \times 10^{-8}} = 3.59 \times 10^{6} \\ R_{PET} &= \frac{0.13}{1.67 \times 10^{-10}} = 7.78 \times 10^{8} \\ R &= 7.82 \times 10^{8} \end{aligned} \]

\[ \begin{aligned} \text{flow} &= \frac{6.25 \times 0.30}{7.82 \times 10^{8}} = 2.40 \times 10^{-9}\ \text{cm}^{3}/\text{s} \\ t &= \frac{0.025}{2.40 \times 10^{-9}} = 1.04 \times 10^{7}\ \text{s} \approx 121\ \text{days} \end{aligned} \]

The thicknesses must be in cm (0.15 and 0.13) to match the permeability units. The PET layer gives almost all the resistance, so PET alone would allow about 120 days; the shorter shelf lives of 103, 73 and 61 days would need a faster leak than the two layers together permit.