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The cost in millions of dollars for a company to manufacture 𝑥 thousand automobiles is given by the function 𝐶(𝑥) = 5𝑥 2 − 40𝑥 + 98. a. How many automobiles must the company produce to minimize the cost? b. How many automobiles is the company currently producing if the cost is $75.8 million? c. What is the company’s cost if it produces 8000 automobiles?

 Dec 16, 2020
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a.  We have the form   ax^2  + bx  + c

 

The number of autos that minimize  the cost is   -b /2a   =   - (-40)  / (2 (5) )   =  40  / 10  =  4  (thousand)

 

 

b.  75.8 = 5x^2  - 40x +  98       subtract  75.8  from both sides

 

5x^2  - 40x  + 22.2  =  0

 

Quadratic function 

x  =   [ 40  ±  sqrt ( 40^2  - 4 (5) (22.2) ) ]/  (2 * 5)   =  .6 or 7.4 = 600  or 7400   autos....note both ptoduction  levels give the  same  cost

 

c.   5(8)^2  - 40 (8)  +  98    =  98 (million dollars)

 

 

cool cool cool     

 Dec 16, 2020

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