Question 710637
A company producing steel construction bars uses the function R(x) = -0.06x^2+10.2x -50 to model the unit revenue in dollars for producing x bars. For what number of bars is the revenue at a maximum?
Because the leading coefficient is negative, we KNOW the parabola opens downwards.  This means the vertex is the MAXIMUM.
the x-value of the vertex is:
x = -b/(2a)
x = -10.2/(2*(-0.06))
x = -10.2/(-0.12)
x = 85 bars
.
What is the unit revenue at that level of production?
find the revenue by plugging it back into the original equation:
R(x) = -0.06x^2+10.2x -50
R(85) = -0.06(85)^2+10.2(85) -50
R(85) = -433.5 + 867 - 50
R(85) = $383.50