The car company has found that the revenue from sales of sedans is a function of the unit price p, in dollars, that it charges. If the revenue R, in dollars is R(p) = 1900p − 0.5p2 (i) At what prices p is revenue zero? (ii) For what range of prices will revenue exceed $1.2 million?
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R(p) = 1900p − 0.5p²
(i) Find the price when the revenue = 0
1900p − 0.5p² = 0
p(1900 - 0.5p) = 0
p = 0 or 0.5p = 1900
p = 0 or p = 3800
Answer: The revenue is zero when the price is zero or when the price is at Rs 3800
(ii) Find the price when the revenue exceed $1.2 million
1900p − 0.5p² > 1, 200, 000
0.5p² - 1900p + 1200000 < 0
p² - 3800p + 2400000 < 0
(p - 800)(p - 3000) < 0
⇒ price range is from Rs 800 to Rs 3000
Answer: The price has to be within the range of Rs 800 to Rs 3000 to exceed $1.2 million.
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