$.(8$ points$)$ A multi$-$sector model Consider a version of the manufacturing bid$-$rent curve, but with two sectors$.$ Let x$1$ and x$2$ be the distance that firms in sector $1$ and sector $2$ locate away from the city center. Firms face freight, labor, and land costs $$ but no intermediate goods cost. To simplify the algebra, lets also assume that firms in each sector use only one unit of land $($and thus the land cost, LC$($xi$)=$ P$($xi$)$ for i $=1,2.$ The labor costs for each firm $($as a function of distance to center$)$ is given by: L$($x$1)=20$ A$1$ x$1$ L$($x$2)=30$ A$2$ x$2$ The freight costs for each firm as a function of distance is given by F$($x$1)=($B$1+3)$ x$1$ F$($x$2)=($B$2+3)$ x$2$