$2.$ Design a double sampling plan that has a producers risk of $0\mathrm{.}05$ with AQL $\backslash (1\mathrm{.}5\backslash \%\backslash )$ and consumers risk of $0\mathrm{.}10$ with LQL $\backslash (5\mathrm{.}0\backslash \%\backslash ).$ The lot size is planned to be $2000$ and sample sizes are assumed to be equal. The double sampling plan should satisfy the consumers risk exactly. Explain how this plan works. $(20$ points$)$