When answering Questions $113,$ please consider the following:

The Delta company produces two auto models: SUV and Sedan. The manufacturing process for each is similar in that both require a certain amount of welding and painting. Each SUV takes $3$ hours of welding and $2$ hours of painting. Each sedan must go through $2$ hours and $1$ hour of painting. During the next production period, $240$ hours of welding time and up to $140$ hours of painting time may be used. Each SUV sold yields a profit of $25$ hundred dollars. Each sedan assembled may be sold for a $$10$ hundred dollars. Formulate and solve this LP production mix situation to find the best combination of SUVs and sedans that yields the highest profit. Please use X$1$ for the quantity of SUVs and X$2$ for the quantity of sedans. For profits, please use the unit of a hundred dollars.