Answer
The largest weekly profit is ${{\$}} 2700$ per week,
when the unit price is ${{\$}} 8.00$ per T-shirt.
Work Step by Step
$P=R-C$
$P=-50x^{2}+800x-500$.
The graph of P(x) is a parabola opening down.
The largest monthly profit occurs at the vertex, when
$x=-b/(2a)=-\displaystyle \frac{800}{-2\times 50}= {{\$}} 8$
The corresponding weekly profit is
$P=-50(8)^{2}+800(50)-500 ={{\$}} 2700$ per week.