Learning activities : The boundaries and application functions
The following exercises are training activities for students to practice and reinforce their skills.
Activity 1 . Maximizing average cost
The average monthly cost because a computer assembly company assembled units is given by the following function:
Cu = 15000 + 1250u
Where u represents the number of assembled units . They want to increase the number of assembled units. Determine the maximum average cost of the firm if production assembly units is increased.
The average monthly cost is given by the function C ( u) = 15,000 +1,250 / u
The average monthly cost function to left : C ( x ) = aX + Cf to determine the fixed cost.
Substituting C ( x ) = 15,000 x +1.250
The average monthly cost equals total cost by the number of assembled units contributing to the cost .
The average cost function : Cm ( x ) = Cx / x
Substituting C ( x ) = ( [ 15,000 x / x ] + [ 1250 / x ] ) = 15,000 +1250 / x =
C ( u) = 15,000 +1,250 / u
The average monthly cost function has 15,000 without the u, because each unit will cost 15,000 more , and fixed costs that do not change .
As the number of assembled units is not defined , it is considered infinite and function tends to 15,000 .
In the equation is defined which approaches infinity , so that by substituting the value of u in the same , any number divided by infinity is zero , so that the fixed cost from infinity ( 1250/infinito ) gives zero
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