Question

If the cost C, cod manufacturing x units of a certain product is given Find the number of units manufactured at a cost of $13,260 There are ? units

Answer 1

We are given that the cost of manufacturing "x" units is given by the following formula:

`C(x)=x^2+10x+60`

We are asked to determine the number of units "x" for a cost C = $13260. To do that we will replace the value of "C" in the equation for 13260:

`13260=x^2+10x+60`

Now we subtract 13260 from both sides, we get:

`\begin{gathered} 13260-13260=x^2+10x+60-13260 \\ 0=x^2+10x-13200 \end{gathered}`

Now, to solve this equation we will factor the equation. To do that we re write the factors as this:

`(x\cdot\cdot)(x\cdot\cdot)=0`

Now we need to determine two numbers which product ios -13260 and which algebraic sum is 10, those numbers are 120 and -110, since:

`\begin{gathered} 120*(-110)=-13260 \\ 120-110=10 \end{gathered}`

Replacing the number we get:

`(x+120)(x-110)=0`

Now we set each factor to zero and solve for "x":

`\begin{gathered} x+120=0 \\ x=-120 \\ \end{gathered}`

The second factor is:

`\begin{gathered} x-110=0 \\ x=110 \end{gathered}`

Since the number of units should be a positive number we get that the number of units must be 110.