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If the cost c , for manufacturing x units of a certain product is given by c=x to the second power -5x+70, find the number of units manufactured at a cost of $8620 There are ? units manufactured at a cost of $8620

If The Cost C For Manufacturing X Units Of A Certain Product Is Given By Cx To The Second Power 5x70 Find The Number Of Units Manufactured At A Cost Of 8620 The class=

Answer :

Setting c=8620 we get:

[tex]\begin{gathered} 8620=x^2-5x+70, \\ x^2-5x-8550=0. \end{gathered}[/tex]

Now, notice that:

[tex]\begin{gathered} -8550=-95\times90, \\ -5=-95+90. \end{gathered}[/tex]

Then:

[tex]x^2-5x-8550=x^2-95+90-95\times90=(x-95)(x+90)\text{.}[/tex]

Therefore:

[tex]x^2-5x-8550=0\Leftrightarrow x=95\text{ or x=-90.}[/tex]

Since x=-90 does not have real meaning, we get that x=95.

Answer: There are 95 units manufactured at a cost of $8620.

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