Suppose your tile company spends $ 195 each month, regardless of how many tiles are purchased as supplies. How much do you spend if you purchase 1000 tiles this month, taking into account this fixed cost?
c. What is a possible reason for this fixed cost?
d. Find the cost equation for the tile. Let x represent the quantity of tiles purchased. Set m equal to the cost of each tile. Set b as the fixed cost. Write your answer in the form C = mx + b. (Do not substitute a value for a x. We need x as a variable.)
e. Use your equation from part c and substitute x = 2000. What does your answer represent ?
f. Why is the cost of each tile multiplied by the quantity of tiles purchased? Why isn't the fixed cost multiplied by x?
To calculate the total cost spent on tiles while taking into account the fixed cost, you can use the equation C = mx + b, where C represents the total cost, m represents the cost of each tile, x represents the quantity of tiles purchased, and b represents the fixed cost.
In this case, we are given that the fixed cost is $195 each month, regardless of the quantity of tiles purchased. Therefore, b = $195.
So the cost equation for the tiles would be C = mx + $195.
Now, let's substitute x = 1000 into the equation to find the total cost spent on 1000 tiles.
C = m * 1000 + $195
The answer represents the total cost spent on purchasing 1000 tiles, including the fixed cost of $195.
Now, let's address why the cost of each tile is multiplied by the quantity of tiles purchased (mx) while the fixed cost is not multiplied by x.
The cost of each tile (m) is multiplied by the quantity of tiles purchased because as the number of tiles increases, the cost increases proportionally (assuming the cost per tile remains constant). So mx represents the variable cost component that changes depending on the quantity of tiles.
On the other hand, the fixed cost (b) does not depend on the quantity of tiles, but rather it remains constant regardless of the number of tiles purchased. That's why it's not multiplied by x in the equation.