Question

the marginal cost of producing x items is 1.35-0.003x. what is the cost of producing 125 items if the cost of producing one item is 270$

Answer 1

Given :  The marginal cost  (dollars per item) of  producing x items is 1.35-

0.003x. cost of  producing one item is $270

To Find : cost of producing 125  items

Solution:

M(x)  = 1.35 - 0.003x

C(x) = ∫M(x)dx

C(x) = ∫(1.35 - 0.003x)dx

=> C(x) = 1.35x - 0.003 x²/2  + k

=>  C(x) = 1.35x - 0.0015 x² + k

cost of  producing one item is  $270

=> C(1) = 1.35 - 0.0015 + k = 270

=> k =268.6515

   C(125) =  1.35(125) - 0.0015(125)² + k  

=> C(125) =  1.35(125) - 0.0015(125)² + 268.6515

=>   C(125) = 413.964

cost of producing 125  items  = 413.96  $

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