Question

The marginal cost function of a firm is 2+3e^x , where x is output . Find the total cost function and total average cost function if the fixed cost is 500

Answer 1

Answer:

⇒  We have, C(x)=2x  

2

−4x+5.

⇒   Average cost =  

x

C(x)

​

 

⇒    Average cost =  

x

2x  

2

−4x+5

​

 

⇒    Average cost = 2x−4+  

x

5

​

 

⇒    Now, substitute value of x=2.

⇒    Average cost = 2(2)−4+  

2

5

​

=  

2

5

​

Step-by-step explanation:

Answer 2

Concept:

An integral is a mathematical notion that explains displacement, area, volume, and other ideas that come from the combination of infinitesimal data. Integration is the term used to describe the process of locating integrals.

Given:

The marginal cost function is 2 +3eˣ.

The fixed cost is 500.

Find:

The total cost function and total average cost.

Solution:

The marginal cost function = 2+3eˣ.

The total cost function f(x) = $\int\limits^._. {2+3e^x} \, dx$.

                                     f(x)  = 2x + 3eˣ +c

The fixed cost is 500 at f(0).

f(0) = 2*0 + 3e⁰+ c

500 = 3 + c

c = 497.

The total cost function f(x) = 2x + 3eˣ + 497.

The total average cost = $\frac{f(x)}{x}$

                                      =$\frac{2x+3e^x+497}{x}$

                                      = $2 + 3\frac{e^x}{x}+\frac{497}{x}$

Hence, The total cost function is 2x + 3eˣ + 497 and total average cost function is $2 + 3\frac{e^x}{x}+\frac{497}{x}$.