A manufacturer discovered that this marginal cost is 6q + 1 dollars per unit whenq units are produced. The total cost (including overhead) of producing the firstunit is $ 130. What is the cost of producing the first 10 units?a) US$345b)US$234c) US$525d) US$436

Answered: A manufacturer discovered that this…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A manufacturer discovered that this marginal cost is 6q + 1 dollars per unit when
q units are produced. The total cost (including overhead) of producing the first
unit is $ 130. What is the cost of producing the first 10 units?
a) US$345
b)US$234
c) US$525
d) US$436

Expert Solution

Step 1

The change in the total cost, when one additional unit of a product is sold is called the marginal cost. Marginal cost is calculated by dividing the change in the total cost by the change in the quantity.

A differential equation can be solved using the variable separation method. In this method, the terms with like variables are isolated on either side of the equation and then integrated with respect to the variables to yield the general solution.

It is known that $\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C$ . Here, C is the integration constant.