To find the flat fee for delivery, we need to determine the value in the provided equation [tex]\(y - 3000 = 0.25(x - 10000)\)[/tex]. This equation describes the relationship between the total cost [tex]\(y\)[/tex] and the number of tiles [tex]\(x\)[/tex] sold.
First, rewrite the equation in the form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the cost per tile and [tex]\(b\)[/tex] is the flat fee. Let’s start by expanding and rearranging the given equation:
1. Starting with the given equation:
[tex]\[
y - 3000 = 0.25(x - 10000)
\][/tex]
2. Distribute the [tex]\(0.25\)[/tex]:
[tex]\[
y - 3000 = 0.25x - 0.25 \times 10000
\][/tex]
[tex]\[
y - 3000 = 0.25x - 2500
\][/tex]
3. Add [tex]\(3000\)[/tex] to both sides to isolate [tex]\(y\)[/tex]:
[tex]\[
y = 0.25x - 2500 + 3000
\][/tex]
4. Combine the constant terms:
[tex]\[
y = 0.25x + 500
\][/tex]
So, the function that describes the revenue [tex]\(y\)[/tex] of the tile factory in terms of [tex]\(x\)[/tex] tiles sold is:
[tex]\[
y = 0.25x + 500
\][/tex]
From this equation, we can directly see the flat fee for delivery in the constant term.
Therefore, the flat fee for delivery is:
[tex]\[
\$ 500
\][/tex]
