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

Question

asked Dec 12, 2023 67.1k views

1 Answer

Karthick Aravindan · Answer 1 · 2023-12-17T14:48:03+0000

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

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:

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:

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.