The supply function for a commodity is p = x^2 + x + 3. The producer's surplus when x = 3 is Option 1: 45/2 Option 2: 32/3 Option 3: 45 Option 4: 62/3

Answer: 45/2. Solution: At x = 3, p_0 = 9+3+3 = 15. Producer's surplus = x_0p_0 - _0^3 (x^2+x+3)dx = 45 - (9 + 9/2 + 9) = 45 - 45/2 = 45/2.

Calculus

Application of Integrals

Medium

applied

The supply function for a commodity is $p = x^2 + x + 3$ . The producer's surplus when $x = 3$ is,

$\frac{45}{2}$

$\frac{32}{3}$

$\frac{62}{3}$

✅ Correct Option: 1

At $x = 3$ , $p_0 = 9+3+3 = 15$ . Producer's surplus $= x_0p_0 - \int_0^3 (x^2+x+3)dx = 45 - \left(9 + \frac{9}{2} + 9\right) = 45 - \frac{45}{2} = \frac{45}{2}$ .

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Solution

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The supply function for a commodity is $p = x^2 + x + 3$ . The producer's surplus when $x = 3$ is,