A Manufacturer of Digital Audio Players Estimates That the Profit $P = - 76 x ^ { 3 } + 4830 x ^ { 3 } - 320,000,00 \leq x \leq 60$

Multiple Choice

A manufacturer of digital audio players estimates that the profit for selling a particular model is $P = - 76 x ^ { 3 } + 4830 x ^ { 3 } - 320,000,00 \leq x \leq 60$ , where $P$ is the profit in dollars and $x$ is the advertising expense in 10,000 's of dollars (see figure) . Find the smaller of two advertising amounts that yield a profit $P$ of $\$ 2,100,000$ . Round your answer to the nearest dollar. Advertising expense (in 10,000 s of dollars)

A) $\$ 460,892$
B) $\$ 315,369$
C) $\$ 363,471$
D) $\$ 512,458$
E) $\$ 384,356$