Question

An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If X engines are made, then the unit cost is given by the function C(x)=0.2$x^{2}$-36x+17,550. What is the minimum unit cost? Do not round your answer. Will report fake answers.

Answer 1

Given :   The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made.  x  = engines   made,  C(x)=0.2x²-36x+17,550

To find : minimum unit cost

Solution:  

C(x) = 0.2x²  - 36x + 17,550

dC/dx = 0.4x  - 36

put dC/dx = 0

=> 0.4x  - 36  = 0

=> 0.4x = 36

=> x = 90

d²C/dx² = 0.4 > 0

Hence at x = 90

Cost will be minimum

C(90) = 0.2(90)²  - 36(90) + 17,550

= 1,620 - 3240 + 17,550

= 15930 $

minimum unit cost =  15930 $

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