11. A company's market research department recommends the manufacturer and marketing of a new headphone set for MP3 players. After suitable test marketing, the research department presents the following price-demand equation:
\( x = 10000 - 1000 p\)
where \(x\) is the number of headphones that retailers are likely to buy at RM \(p\) per set. The financial department provides the cost function.
\(C ( x ) = 7000 + 2 x\)
a. Find the domain of the function defined by the price-demand equation. b. Find and interpret the marginal cost function c. Find the marginal revenue at \( x = 2000,5000 \) and \( 7000 \) . Interpret these results d. Find the marginal profit at \( x = 1000,4000 \) , and \( 6000 \) . Interpret these results.