suppose you right a book. the printer charges $4 per book to print it, and you spend #3500 on advertising. you sell the book for $15 a copy. how many copies must you sell so that your income from sales is greater than your total cost?
costs= fixed cost + variable cost
income=15*books
if income is > than costs
15*B>3500+4B
11B>3500
B>327, so B must be 328 so that income is greater than costs.
To find out how many copies you need to sell in order to have income from sales greater than your total cost, we can set up an equation.
Let's denote the number of copies sold as 'x'.
The total cost is the sum of the printing cost and advertising cost:
Total cost = Printing cost + Advertising cost
Total cost = $4 * x + $3500
The income from sales is the product of the selling price and the number of copies sold:
Income from sales = Selling price * Number of copies sold
Income from sales = $15 * x
Since you want the income from sales to be greater than the total cost, we can form the equation:
Income from sales > Total cost
$15 * x > $4 * x + $3500
Now, we can solve for 'x':
$15 * x - $4 * x > $3500
$11 * x > $3500
x > $3500 / $11
By dividing $3500 by $11, we get:
x > 318.18
Since you cannot sell a fraction of a book, you need to round up the value of 'x' to the next whole number.
Therefore, you need to sell at least 319 copies of the book in order for your income from sales to be greater than your total cost.
To find out how many copies you need to sell, we can use the equation:
Income from Sales > Total Cost
Let's break down the components:
Total Cost = Cost of printing + Advertising cost
Income from Sales = Revenue from selling the book
Given information:
Cost of printing = $4 per book
Advertising cost = $3500
Selling price = $15 per copy
Now, let's substitute these values into the equation:
Revenue from selling the book = Selling price × Number of copies sold
The equation becomes:
$15 × Number of copies sold > $4 × Number of copies sold + $3500
To solve for the number of copies, let's manipulate the equation:
$15 × Number of copies sold - $4 × Number of copies sold > $3500
$11 × Number of copies sold > $3500
Now, we can solve for the number of copies sold:
Number of copies sold > $3500 ÷ $11
Number of copies sold > 318.18
Since you cannot sell a fraction of a book, you must round up the number of copies. Therefore, you must sell at least 319 copies to have your income from sales greater than your total cost.