Design a double sampling plan that has a producers risk of $0\mathrm{.}05$ with AQL $2\mathrm{.}5\%$ and consumers risk of $0\mathrm{.}10$ with LQL $7\mathrm{.}0\%.$ The lot size is planned to be $2800$ and sample sizes are assumed to be equal. The double sampling plan should satisfy the producers risk exactly.