Question

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

Answer 1

Setting c=8620 we get:

`\begin{gathered} 8620=x^2-5x+70, \\ x^2-5x-8550=0. \end{gathered}`

Now, notice that:

`\begin{gathered} -8550=-95*90, \\ -5=-95+90. \end{gathered}`

Then:

`x^2-5x-8550=x^2-95+90-95*90=(x-95)(x+90)\text{.}`

Therefore:

`x^2-5x-8550=0\Leftrightarrow x=95\text{ or x=-90.}`

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

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