Question 824302
Take the derivative and set it = to 0 to find the max.<P>
Derivative of {{{ -0.04x^2+6.8x -100}}} = -.08x + 6.8 = 0<P>
-.08x = -6.8<P>
x = 85<P>
Verify it's a max by looking at the value of the derivative for the interval -inf to 85 and 85 to inf.  If 85 is a max, the derivative will be positive before 85 and negative after 85.<P>
0 is in the first interval:  -.08*0 + 6.8 is positive.<P>
100 is in the second interval: -.08*100 + 6.8 = -8 + 6.8 is negative.<P>
The graph is rising before x=85 and falling after x=85, so 85 is a maximum.
Plug 85 into the equation to find the unit revenue.<P>
{{{ -0.04*(85^2)+6.8(85) -100 = 189}}}