Question

The total cost producing q units of certain product is described by the function
C = 1,000,000 + 15,000q + 2.5q2
Where C is the total cost stated in dollars.
Determine how many units q should be produced in order to minimize the average cost per unit
b. What is the minimum average cost per unit?
c. What is the total cost of production at this level output?

Answer 1

• 1,000,000plus15,000plus2.5q2

Answer 2

Given : The total cost producing q units of certain product is described by the function

C = 1,000,000 + 15,000q + 2.5q²

To Find  : a) Determine how many units q should be produced in order to minimize the average cost per unit

b. What is the minimum average cost per unit?

c. What is the total cost of production at this level output?

Solution:

C = 1,000,000 + 15,000q + 2.5q²

C/q   =  1,000,000/q + 15,000  + 2.5q

 A = C/q  =    average cost per unit

A =   1,000,000/q + 15,000  + 2.5q

dA/dq  =  -1,000,000/q²  + 0 + 2.5

=>  dA/dq  =  -1,000,000/q²  + 2.5

dA/dq  =  0

=> -1,000,000/q²  + 2.5  = 0

=> q²  = 4,00,000

=> q = 632.45

d²A/dq²  =  2,000,000/q³  > 0

Hence A is minimum when q = 632.45

632 units will give minimum average cost per unit

A =   1,000,000/q + 15,000  + 2.5q   = 18162.28  $ per unit   at 632 output

C = 1,000,000 + 15,000q + 2.5q²  =  11478560   $  total cost of production at 632 output

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