The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company’s fixed costs allotted to this product is $300, and the supplier’s cost for a set of tile is $6 each. Let x represent the number of tile sets.
c. If b represents a fixed cost, what value would represent b?
b=$300
d. Find the cost equation for the tile. Write your answer in the form C = mx + b.
C=6x+300
The profit made from the sale of tiles is found by subtracting the costs from the revenue.
e. Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation.
P=(-x +62x)-(6x+300)
f. What is the profit made from selling 20 tile sets per month?
g. What is the profit made from selling 25 tile sets each month?
h. What is the profit made from selling no tile sets each month? Interpret your answer.
i. Use trial and error to find the quantity of tile sets per month that yields the highest profit.
j. How much profit would you earn from the number you found in part i?
k. What price would you sell the tile sets at to realize this profit (hint, use the demand equation from part a)?
2. The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values.
3. In 2002, Home Depot’s sales amounted to $58,200,000,000. In 2006, its sales were $90,800,000,000.
a. Write Home Depot’s 2002 sales and 2006 sales in scientific notation.
You can find the percent of growth in Home Depot’s sales from 2002 to 2006, follow these steps:
• Find the increase in sales from 2002 to 2006.
• Find what percent that increase is of the 2002 sales.
b. What was the percent growth in Home Depot’s sales from 2002 to 2006? Do all your work by using scientific notation.
I don't know what your question is, or what "c" is, but the total cost of producing x tile sets will be
C = 300 + 6x
To find the profit made from selling 20 tile sets per month, substitute x = 20 into the profit equation P = (-x + 62x) - (6x + 300).
P = (-20 + 62(20)) - (6(20) + 300)
P = (-20 + 1240) - (120 + 300)
P = 1220 - 420
P = 800
Therefore, the profit made from selling 20 tile sets per month is $800.
To find the profit made from selling 25 tile sets each month, substitute x = 25 into the profit equation P = (-x + 62x) - (6x + 300).
P = (-25 + 62(25)) - (6(25) + 300)
P = (-25 + 1550) - (150 + 300)
P = 1525 - 450
P = 1075
Therefore, the profit made from selling 25 tile sets per month is $1075.
To find the profit made from selling no tile sets each month, substitute x = 0 into the profit equation P = (-x + 62x) - (6x + 300).
P = (-0 + 62(0)) - (6(0) + 300)
P = 0 - 0
P = 0
Therefore, the profit made from selling no tile sets per month is $0. This means that there is no profit or loss when no tile sets are sold.
To find the quantity of tile sets per month that yields the highest profit, you can use trial and error by substituting different values of x into the profit equation and calculating the corresponding profit.
To find the profit at each value, substitute the different values of x into the profit equation P = (-x + 62x) - (6x + 300).
For example, when x = 1:
P = (-1 + 62(1)) - (6(1) + 300)
P = (-1 + 62) - (6 + 300)
P = 61 - 306
P = -245
When x = 5:
P = (-5 + 62(5)) - (6(5) + 300)
P = (-5 + 310) - (30 + 300)
P = 305 - 330
P = -25
And so on...
Continue substituting different values of x and calculate the corresponding profit until you find the quantity of tile sets per month that yields the highest profit.
To find the profit earned from the number you found in part i, you can substitute that value of x into the profit equation P = (-x + 62x) - (6x + 300) and calculate the profit.
For example, if the value of x from part i is x = 15:
P = (-15 + 62(15)) - (6(15) + 300)
P = (-15 + 930) - (90 + 300)
P = 915 - 390
P = 525
Therefore, the profit earned from the number found in part i is $525.
To determine the price to sell the tile sets at to realize this profit, you would need additional information such as the demand equation mentioned in part a. Without that information, it is not possible to calculate the selling price.
To find the break-even values for a profit model, you need to solve the profit equation P = 0. Substitute P = 0 into the profit equation P = (-x + 62x) - (6x + 300) and solve for x.
0 = (-x + 62x) - (6x + 300)
0 = 56x - 6x - 300
0 = 50x - 300
50x = 300
x = 6
Therefore, the break-even value for the quantity of tile sets per month is x = 6.
In scientific notation, Home Depot's 2002 sales of $58,200,000,000 can be written as 5.82 x 10^10 and Home Depot's 2006 sales of $90,800,000,000 can be written as 9.08 x 10^10.
To find the percent growth in Home Depot's sales from 2002 to 2006, you can follow these steps:
Step 1: Find the increase in sales from 2002 to 2006.
Increase = 9.08 x 10^10 - 5.82 x 10^10
Step 2: Find what percent that increase is of the 2002 sales.
Percent growth = (Increase / 5.82 x 10^10) * 100
Perform the calculations using scientific notation to determine the percent growth in Home Depot's sales from 2002 to 2006.