Question

Consider the following situation: you are running a business, and you make an initial investment
Rs. 100,000. It costs you Rs. 12,000 to manufacture each item
i. Write a function to model your total costs.
ii. Write a function to model the average cost per item. Use a graphing utility to determine
the minimum of this function. What does this mean?

Answer 1

Given  : initial investment Rs. 100,000.

costs Rs. 12,000 to manufacture each item  

To Find :

i. Write a function to model your total costs.

ii. Write a function to model the average cost per item. Use a graphing utility to determine

the minimum of this function. What does this mean?

Solution:

C(x)  = Total  Cost function

x is the Quantity Produced

Cost  = Fixed Cost +  number of items * cost per item

=> C(x)  = 100000  + 12000x

C(x)  = 100000  + 12000x   is Total cost function

average cost per item  =  C(x)/x    

= (100000  + 12000)/x

= 100000/x  + 12000

 minimum of this function. ≈ 12000

 when x → ∞

As the production increases average cost reduces

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