To find the maximum profit given by the function \( P(g) = -5g^2 + 30g + 50 \), we recognize that this is a quadratic function of the form \( P(g) = ax^2 + bx + c \), where \( a = -5 \), \( b = 30 \), and \( c = 50 \).
Since the coefficient of \( g^2 \) (which is \( a = -5 \)) is negative, the parabola opens downwards, which means the vertex of the parabola will give us the maximum profit.
The \( g \)-coordinate of the vertex of a quadratic function can be found using the formula:
\[ g = -\frac{b}{2a} \]
Substituting the values of \( a \) and \( b \):
\[ g = -\frac{30}{2(-5)} = -\frac{30}{-10} = 3 \]
Now that we have \( g = 3 \), we can find the maximum profit by substituting \( g \) back into the profit function \( P(g) \):
\[ P(3) = -5(3^2) + 30(3) + 50 \]
Calculating \( P(3) \):
\[ P(3) = -5(9) + 90 + 50 \] \[ P(3) = -45 + 90 + 50 \] \[ P(3) = 45 + 50 = 95 \]
Thus, the maximum profit that can be made is \( 95 \) thousand dollars.
Therefore, the maximum profit is:
\[ \boxed{95} \]