Question $3$: $(40$ points$)$

Formulate an LP model for the following problem. $($Do not solve$)$

Toolco has contracted with AutoMate to supply their automotive discount stores with wrenches and chisels. AutoMate's weekly demand consists of at least $1570$ wrenches and $1250$ chisels. Toolco cannot produce all the requested units with its present one$-$shift capacity and must use overime and possibly subcontract with other tool shops. The result is an increase in the production cost per unit, as shown in the following table. Market demand restricts the ratio of chisels to wrenches to at least $2$:$1$

$\backslash$table$[[$Tool$,$Production Type,$\backslash$table$[[$Weekly$],[$Production$],[$Range $($units$)]],$Unit Cost $($$$)],[$Regular$,0-500,2\mathrm{.}00],[$Overtime$,501-800,2\mathrm{.}80],[,$Subcontracting,$801-,3\mathrm{.}00],[$Chisels$,$Regular,$0-620,2\mathrm{.}10],[$Overtime$,621-900,3\mathrm{.}20],[$Subcontracting$,901-,4\mathrm{.}20]]$