Calculus

Application of Integrals

Hard

applied

The supply function of a producer is given by $p = \frac{3}{5}e^{3x}$ , where $x$ denotes a thousand units. If sales are 4000 units, then the producers' surplus is

$\frac{11}{7}e^{11}$

$\frac{11}{6}e^{12}$

$\frac{11}{5}e^{12} + \frac{1}{5}$

$\frac{11}{4}e^{11} + \frac{1}{5}$

✅ Correct Option: 3

With 4000 units, $x_0=4$ and $p_0=\frac35e^{12}$ . Producer surplus $=x_0p_0-\int_0^4\frac35e^{3x}dx=\frac{12}{5}e^{12}-\frac15\left(e^{12}-1\right)=\frac{11}{5}e^{12}+\frac15$ .

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The supply function of a producer is given by p=35e3xp = \frac{3}{5}e^{3x}p=53​e3x, where xxx denotes a thousand units. If sales are 4000 units, then the producers' surplus is

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CUET Mathematics Past Year Questions (Topic-Wise)

The supply function of a producer is given by $p = \frac{3}{5}e^{3x}$ , where $x$ denotes a thousand units. If sales are 4000 units, then the producers' surplus is