The marginal cost of production (in Rs.) is x .e x 03 0 3000 3 , where x denotes the number of units. The cost of producing 100th unit is:
To find the cost of producing the 100th unit, we can substitute the value of x as 100 and calculate the value of the expression.
Substituting x = 100 in the given expression:
Marginal cost of production = x.e^(x^2) - 3000x^3 + 3000
= 100.e^(100^2) - 3000(100^3) + 3000
Now, it's important to note that the value of e^(100^2) is quite large and may not be able to be accurately calculated using regular calculators. In this case, we can use the approximation value of e^(100^2) ≈ 2.68811e+130.
Substituting this approximation:
Marginal cost of production = 100 * 2.68811e+130 - 3000(100^3) + 3000
= 2.68811e+132 - 3000(100^3) + 3000
Now, calculate the value of 100^3:
100^3 = 100 * 100 * 100 = 1,000,000
Substituting this value:
Marginal cost of production = 2.68811e+132 - 3000(1,000,000) + 3000
= 2.68811e+132 - 3,000,000,000 + 3000
Finally, calculate the cost of producing the 100th unit:
Cost of producing the 100th unit = 2.68811e+132 - 3,000,000,000 + 3000
Please note that the final value may be very large and will require using scientific notation to express it accurately.