Green Vehicle Inc., manufactures electric cars and small delivery trucks. It has just opened a new factory where the C$1$ car and the T$1$ truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes $1/30$ of a day and $1/80$ of a day to paint a truck of type T$1$ and a car of type C$1$ in the paint shop, respectively. It takes $1/50$ of a day to assemble either type of vehicle in the assembly shop.

A T$1$ truck and a C$1$ car yield profits of $$325$ and $$220,$ respectively, per vehicle sold.

Formulate the linear program that provides the combination of T$1$ and C$1$ that maximizes yield, clearly specifying $($a$)$ variables, $($b$)$ objective function and $($c$)$ constraints