Dye Dilution Is a Method of Measuring Cardiac Output $A \mathrm { mg }$

Dye dilution is a method of measuring cardiac output. If $A \mathrm { mg }$ of dye is used and $c ( t )$ is the concentration of the dye at time $t$ , then the cardiac output over the time interval $[ 0 , T ]$ is given by
$$F = \frac { A } { \int _ { 0 } ^ { T } c ( t ) d t }$$
Find the cardiac output over the time interval $[ 0,15 ]$ if the dye dilution method is used with $10 \mathrm { mg }$ of dye and the dye concentration, in $\mathrm { mg } / \mathrm { L }$ , is modeled by
$$c ( t ) = \frac { 1 } { 2 } t ( 15 - t ) , 0 \leq t \leq 15$$
where $t$ is measured in seconds.

A) $\quad 0.029$
B) $0.039$
C) $0.026$
D) $0.044$
E) $0.036$
F) $0.020$