$2(2$ points$)$ A large retirement village has a total retail employment of $120.$ All $1600$ of the households in this village consist of two nonworking family members with household income of $$20,000.$ Assuming that shopping and social$/$recreational trip rates both peak during the same hour $($for exposition purposes$),$ village using the trip generation model below:

Number of peak$-$hour vehicle$-$based shopping trips per household $=0\mathrm{.}12+0\mathrm{.}09($household size$)+0\mathrm{.}011($annual household income in thousands of dollars$)-0\mathrm{.}15($employment in the household's neighborhood, in hundreds$)$

Number of peak$-$hour vehicle$-$based social$/$recreational trips per household $=0\mathrm{.}04+0\mathrm{.}018($household size$)+0\mathrm{.}009($annual household income in thousands of dollars$)+0\mathrm{.}16($number of nonworking household members$)$

a$.$ Predict the total number of peak$-$hour trips generated by this village

b$.$ Determine the amount of additional retail employment $($in the village$)$ necessary to reduce the total predicted number of peak$-$hour shopping trips to $200$