$1-$ Use MIL$-$STD$-105$E to design a single normal acceptance sampling plan for inspecting a lot of $5000$ items using inspection level III and acceptable quality level of $0\mathrm{.}40\%.$

$2-$ If the producer's risk of the sampling plan you designed in part $1$ is too high but the customer's risk is substantially lower than requirement, how can you modify this single sampling plan to lower the producer's risk taking into consideration that due to the limitation on resources, sample size cannot be increased? Justify your answer?