The gross profit margin is a measurement of a company's manufacturing and distribution efficiency during the production process. If $G$ is the gross profit and $T$ is the total revenue, both in dollars, then the gross profit margin $M=M(G,T)$ is given by the formula

$M=\frac{G}{T}.$

$($a$)$ Use functional notation to express the gross profit margin for a company that has a gross profit of $$335,000$ and a total revenue of $$550,000.$

$($b$)$ Calculate the gross profit margin in part $($a$).$ The gross profit margin is often expressed as a percent. Give your answer as both a decimal and a percent. $($Round your decimal answer to two decimal places, and your percent to the nearest percent.$)$

$M=\%$

$($c$)$ If the gross profit stays the same but total revenue increases, would the gross profit margin increase or decrease?

The gross profit margin will increase.

The gross profit margin will decrease.