The profit made from the sale of tiles is found by subtracting the costs from the revenue. (This is the money you take in minus the money you spent.)
g. Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation. Suppose the revenue equation is R = -x^2+62x.
h. What is the profit made from selling 25 tile sets per month?
i. What is the profit made from selling 30 tile sets each month?
j. What is the profit made from selling no tile sets each month? Why is this value negative?
To find the profit equation, we need to substitute the revenue equation (R) and the cost equation (C) into the formula for profit:
Profit = Revenue - Cost
Given that the revenue equation is R = -x^2 + 62x, and the cost equation is C = 18x + 120, we can substitute these equations into the profit formula:
Profit = (-x^2 + 62x) - (18x + 120)
Now, let's simplify this equation:
Profit = -x^2 + 62x - 18x - 120
To simplify further, we can combine like terms:
Profit = -x^2 + 44x - 120
Now that we have the profit equation, we can use it to find the profit made from selling a certain number of tile sets per month.
For part h, when selling 25 tile sets per month, we can substitute x = 25 into the profit equation:
Profit = -(25)^2 + 44(25) - 120
Simplifying further:
Profit = -625 + 1100 - 120
Profit = 355
Therefore, the profit made from selling 25 tile sets per month is $355.
For part i, when selling 30 tile sets per month, we substitute x = 30 into the profit equation:
Profit = -(30)^2 + 44(30) - 120
Simplifying further:
Profit = -900 + 1320 - 120
Profit = 300
Therefore, the profit made from selling 30 tile sets per month is $300.
For part j, when selling no tile sets per month (x = 0), we substitute x = 0 into the profit equation:
Profit = -(0)^2 + 44(0) - 120
Simplifying further:
Profit = 0 - 0 - 120
Profit = -120
The profit made from selling no tile sets each month is negative because the revenue equation does not offset the cost equation. This means that the cost of producing and selling the tile sets exceeds the revenue earned when no tile sets are sold.