*x= _______ units*

*Determine the maximum revenue. $__________*

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Columbus, MS

R(x) = 312x-0.2x^2 = -0.2x^2+312x. This is the graph of a parabola. To find the # of units x that produce the maximum revenue for this function, we can find the equation for the axis of symmetry. As any parabola can be written in the forn ax^2+bx+c, the axis of symmetry is x= -b/2a. In this case, x= -(312)/2(-0.2) = -312/-0.4 = 780. Therefore
**780 **units produce the maximum revenue, which is R(780)= 312(780) -0.2(780)^2 =
**121680 dollars.**

Miami, FL

Using solver I obtained a similar value.

Objective Cell (Max)

Cell Name Original Value Final Value

$J$5 R(x) = 312x - 0.2x2 311.8 121680

Variable Cells

Cell Name Original Value Final Value Integer

$J$6 x 1 779.9999954 Contin = 780 units.

Constraints

NONE

Cell Name Original Value Final Value

$J$5 R(x) = 312x - 0.2x2 311.8 121680

Variable Cells

Cell Name Original Value Final Value Integer

$J$6 x 1 779.9999954 Contin = 780 units.

Constraints

NONE

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