A computer software retailer has 1200 copies of a new software package to sell. From past experience, she knows that:

- Half of them will sell right away at the original price she sets,
- Two-thirds of the remainder will sell later when their price is reduced by $40 \%$, and
- The remaining copies will sell in a clearance sale at $75 \%$ off the original price.

In order to make a reasonable profit, the total sales revenue must be $\$ 72000$. To the nearest cent, what original price should she set?
(A) $\$ 60.01$
(B) $\$ 75.01$
(C) $\$ 79.13$
(D) $\$ 80.90$
(E) $\$ 240.01$
Let $P$ be the original price the retailer sets.

Then one-half of the initial 1200, or 600 copies, will sell for a price of $P$, giving revenue of $600 P$.

Two-thirds of the remaining 600 , or 400 copies, will sell for a price of $0.6 P$ (ie. $40 \%$ off of $P)$, giving revenue of $400(0.6 P)=240 P$.

The remaining 200 copies will sell for a price of $0.25 P$ (ie. $75 \%$ off of $P$ ), giving revenue of $200(0.25 P)=50 P$.

To make a reasonable profit, her revenue must be $\$ 72000$, or

$$
\begin{aligned}
600 P+240 P+50 P & =72000 \\
890 P & =72000 \\
P & \approx 80.90
\end{aligned}
$$

Thus, she should set an original price of $\$ 80.90$.

Answer: (D)