The marginal cost of production (in Rs) is 3 + x/3000 + e^(-0.03x), where x denotes the number of units. The cost of producing 100th unit is:
put 100 in x
= 3 + 100/3000 + e^(-0.03*100)
= 3 + 0.03333 + e^(-3)
use calculator for e^-3
= 3.03333 + 0.049787068
Ana=3.08
To find the cost of producing the 100th unit, we need to substitute x=100 into the marginal cost equation.
Marginal Cost = 3 + x/3000 + e^(-0.03x)
Substituting x=100:
Marginal Cost = 3 + 100/3000 + e^(-0.03 * 100)
Marginal Cost = 3 + 1/30 + e^(-3)
Now we need to calculate the value of e^(-3). Using a calculator or a computer program:
e^(-3) ≈ 0.0498
Substituting this value into the marginal cost equation:
Marginal Cost = 3 + 1/30 + 0.0498
Marginal Cost = 3 + 0.0333 + 0.0498
Marginal Cost = 3.0831
Therefore, the cost of producing the 100th unit is approximately Rs 3.0831.
To find the marginal cost of producing the 100th unit, we need to substitute x = 100 into the given marginal cost function.
The marginal cost function is: MC(x) = 3 + x/3000 + e^(-0.03x)
Plugging in x = 100, we get:
MC(100) = 3 + 100/3000 + e^(-0.03 * 100)
First, let's simplify the expression 100/3000:
100/3000 = 1/30
Now, let's calculate e^(-0.03 * 100):
e^(-0.03 * 100) ≈ e^(-3) ≈ 0.0498 (rounding to 4 decimal places)
So, plugging in these values, we have:
MC(100) = 3 + 1/30 + 0.0498
Now, let's simplify further:
MC(100) = 3 + 0.0333 + 0.0498
MC(100) ≈ 3.0831 (rounded to 4 decimal places)
Therefore, the cost of producing the 100th unit is approximately Rs 3.0831.