Example 6 - Total revenue received from sale of x units - Examples

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 6 The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant. Marginal revenue is rate of change of total revenue w. r. t the number of unit sold Let MR be marginal revenue Given, R is total revenue. & ๐‘ฅ is number of units sold. So, MR = ๏ท๐‘‘๐‘…๏ทฎ๐‘‘๐‘ฅ๏ทฏ Given, Total revenue = R (๐‘ฅ) = 3๐‘ฅ2 + 36๐‘ฅ + 5 We need to find marginal revenue when ๐‘ฅ = 5 i.e. MR when ๐‘ฅ = 5 MR = ๏ท๐‘‘๏ท๐‘…๏ท๐‘ฅ๏ทฏ๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ MR = ๏ท๐‘‘ ๏ท3๐‘ฅ2 + 36๐‘ฅ + 5๏ทฏ ๏ทฎ๐‘‘๐‘ฅ๏ทฏ MR = ๏ท๐‘‘(3๐‘ฅ2)๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๏ท๐‘‘(36๐‘ฅ)๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๏ท๐‘‘(5)๏ทฎ๐‘‘๐‘ฅ๏ทฏ MR = 3 ๏ท๐‘‘(๐‘ฅ2)๏ทฎ๐‘‘๐‘ฅ๏ทฏ + 36 ๏ท๐‘‘(๐‘ฅ)๏ทฎ๐‘‘๐‘ฅ๏ทฏ + 0 MR = 3 ร— 2๐‘ฅ + 36 MR = 6๐‘ฅ + 36 MR when ๐‘ฅ = 5 MR = 6 (5) + 36 MR = 30 + 36 MR = 66 Hence, the required marginal revenue is Rs. 66

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