Let cost = 600.00 fixed costs
x = set of tiles $11.00
find the profit equation by substituting your equations for R and C P = R -C THE profit made for 26 and 31 tiles per month.
2nd part;
use trail and error to find the quanity of tile sets per month yields the highest profit.
the fundraiser will cost $1.50 per pencil plus $50.00 in advertising. write an equation that represents the cost, c, for n pencils
To find the profit equation, we need to use the given equations for revenue (R) and cost (C) and substitute them into the profit equation P = R - C.
Given:
Fixed costs (C) = $600.00
Cost per tile set (x) = $11.00
Revenue (R) can be calculated using the formula:
R = x * quantity of tile sets per month
Substituting R and C into the profit equation:
P = R - C
P = (x * quantity of tile sets per month) - $600.00
To find the profit made for 26 and 31 tile sets per month, we can substitute the respective quantities into the profit equation:
For 26 tile sets:
P = ($11.00 * 26) - $600.00
P = $286.00 - $600.00
P = -$314.00
For 31 tile sets:
P = ($11.00 * 31) - $600.00
P = $341.00 - $600.00
P = -$259.00
Therefore, the profit made for 26 tile sets per month is -$314.00, and the profit made for 31 tile sets per month is -$259.00.
For the second part of your question, we need to find the quantity of tile sets per month that yields the highest profit using trial and error. By plugging in different quantities and determining which yields the highest profit, we can find the answer.
Here's an example using a few different quantities:
For 10 tile sets:
P = ($11.00 * 10) - $600.00
P = $110.00 - $600.00
P = -$490.00
For 20 tile sets:
P = ($11.00 * 20) - $600.00
P = $220.00 - $600.00
P = -$380.00
For 30 tile sets:
P = ($11.00 * 30) - $600.00
P = $330.00 - $600.00
P = -$270.00
For 40 tile sets:
P = ($11.00 * 40) - $600.00
P = $440.00 - $600.00
P = -$160.00
From these examples, we can see that the quantity of tile sets per month that yields the highest profit is 10, with a profit of -$490.00. However, since this profit is negative, it means that there is no positive profit available with the given fixed costs and tile costs.
Therefore, using trial and error, we conclude that the quantity of tile sets per month does not yield a positive profit.