The revenue R (in dollars)generated by the sale of x units of a digital camera is given by $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$ .Approximate the number of sales that will maximize revenue.
A)Maximum revenue occurs at $x = 4,205$ units.
B)Maximum revenue occurs at $$x = 406$$ units.
C)Maximum revenue occurs at $x = 145$ units.
D)Maximum revenue occurs at $x = 29,435$ units.
E)Maximum revenue occurs at $x = 21,025$ units.

Question

The revenue R (in dollars)generated by the sale of x units of a digital camera is given by $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$ .Approximate the number of sales that will maximize revenue. ​
A)Maximum revenue occurs at $x = 4,205$ units.
B)Maximum revenue occurs at $$x = 406$$ units.
C)Maximum revenue occurs at $x = 145$ units.
D)Maximum revenue occurs at $x = 29,435$ units.
E)Maximum revenue occurs at $x = 21,025$ units.

Quizplus · Accepted Answer

The equation given is in the form of a parabola. The vertex form of a parabola is $(x - h)^2 = 4a(y - k)$, where $(h, k)$ is the vertex of the parabola. In this case, the equation can be rewritten to match this form, with $x - 145$ indicating that the vertex, and thus the maximum revenue, occurs at $x = 145$ units.

The Revenue R (In Dollars)generated by the Sale of X (x−145)2=−57(R−29,435)( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )(x−145)2=−75​(R−29,435)

The Revenue R (In Dollars)generated by the Sale of X $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$