To determine the revenue function and the flat fee for delivery, we start with the given equation:
[tex]\[ y - 3000 = 0.25(x - 10000) \][/tex]
1. Simplify the given equation to get the revenue function:
Begin by distributing the [tex]$0.25$[/tex] on the right-hand side:
[tex]\[ y - 3000 = 0.25x - 2500 \][/tex]
Next, isolate [tex]$y$[/tex] by adding [tex]$3000$[/tex] to both sides of the equation:
[tex]\[ y = 0.25x - 2500 + 3000 \][/tex]
Simplify the right-hand side:
[tex]\[ y = 0.25x + 500 \][/tex]
Thus, the revenue function in terms of the number of tiles sold ([tex]$x$[/tex]) is:
[tex]\[ y = 0.25x + 500 \][/tex]
2. Identify the flat fee for delivery:
The flat fee for delivery is the constant term in the revenue function (the term that does not depend on [tex]$x$[/tex]). In the revenue function [tex]$y = 0.25x + 500$[/tex], the term [tex]$500$[/tex] represents the flat fee for delivery.
Therefore,
- The function that describes the revenue of the tile factory in terms of tiles sold is:
[tex]\[ y = 0.25x + 500 \][/tex]
- The flat fee for delivery is:
[tex]\[ \$500 \][/tex]
