# Calculus1

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User Generated
Subject
Calculus
School
University Of California Los Angeles
Type
Homework
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3.4
1.
a. The function is always increasing since the more units of the commodity is produced, the more it will
cost the company to produce them. This takes into account the cost of labor and capital necessary to
produce the commodity.
b. Based on the graph, the cost per unit begins to increase dramatically at
.
3.
    


a.

and


  

 


  



  

 


   


b. 

and 



 
 

  


  



  





  



  



5.

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  
a. average cost function,
  


b. marginal average cost function,





c. As increases and becomes very large, the total cost also increases and becomes very large. However,
as the total cost and become very large, the average cost or cost per unit becomes smaller and smaller
and approaches zero.
7.
    


a. average cost function,
    

   
b. marginal average cost function,




 


 
9.
  
a. marginal revenue,

 

 

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3.4 1. a. The function is always increasing since the more units of the commodity is produced, the more it will cost the company to produce them. This takes into account the cost of labor and capital necessary to produce the commodity. b. Based on the graph, the cost per unit begins to increase dramatically at 𝑥0 = 4. 3. 𝐶(𝑥) = 2000 + 2𝑥 − 0.0001𝑥 2 (0 ≤ 𝑥 ≤ 6000) a. 𝐶(1001) and 𝐶(2001) 𝐶(1001) = 2000 + 2(1001) − 0.0001(1001)2 𝐶(1001) = 2000 + 2002 − 100.2001 𝐶(1001) = 3901.7999 𝐶(2001) = 2000 + 2(2001) − 0.0001(2001)2 𝐶(2001) = 2000 + 4002 − 400.4001 𝐶(2001) = 5601.5999 b. 𝑀𝐶(1000) and 𝑀𝐶(2000) 𝑀𝐶 = 𝐶 ′ (𝑥) 𝑀𝐶 = 𝐶 ′ (𝑥) = (0) + 2(1) − 2(0.0001𝑥) 𝑀𝐶 = 2 − 0.0002𝑥 𝑀𝐶(1000) = 2 − 0.0002(1000) 𝑀𝐶(1000) = 2 − 0.2 𝑀𝐶(1000) = 1.8 𝑀𝐶(2000) = 2 − 0.0002(2000) 𝑀𝐶(2000) = 2 − 0.4 𝑀𝐶(2000) = 1.6 5. 𝐶(𝑥) = 100𝑥 + 200,000 a. average cost function, 𝐶 𝐶= 𝐶= 𝐶(𝑥) 𝑥 100𝑥 + 200,000 𝑥 𝐶 = 100 + 200,000 𝑥 b. marginal average cost function, 𝐶 ′ 𝐶 ′ = (0) + 200,000(−1)(𝑥 −2 ) 𝐶′ = − 200,000 𝑥2 c. As 𝑥 increases and becomes very large, the total cost also increases and becomes very large. However, as the total cost and 𝑥 become very large, the average cost or cost per unit becomes smaller and smaller and approaches zero. 7. 𝐶(𝑥) = 2000 + 2𝑥 − 0.0001 ...
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