Byron is planning to finance his college education by selling programs at the Kaplan University football games. There is a fixed cost of $400 for printing these programs, and the variable cost is $3. There is also a $1,000 fee paid to the University for the right to sell these programs. If Byron was able to sell programs for $5 each, how many would he have to sell to break even? How many would he have to sell to make a profit of $5,000?

Question

Byron is planning to finance his college education by selling programs at the Kaplan University football games. There is a fixed cost of $400 for printing these programs, and the variable cost is $3. There is also a $1,000 fee paid to the University for the right to sell these programs. If Byron was able to sell programs for $5 each, how many would he have to sell to break even? How many would he have to sell to make a profit of $5,000?

Answer 1

I assume variable cost is cost per program printed. Let x = # programs.

400 + 1000 + 3x = 5x

5000 + 400 + 1000 + 3x = 5x

Solve each for x.

Answer 2

is it 2000

Answer 3

To calculate the number of programs Byron would have to sell to break even, we need to consider the fixed costs, variable costs, and the selling price.

The fixed costs in this case include the cost of printing the programs, which is $400, and the fee paid to the University, which is $1,000. So the total fixed costs are $400 + $1,000 = $1,400.

The variable cost per program sold is $3.

The selling price per program is $5.

To break even, the total revenue should be equal to the total costs.

Let's denote the number of programs Byron needs to sell as 'x'. The total revenue can be calculated by multiplying the selling price by the number of programs sold, so the revenue is 5x.

The total costs include the fixed costs and the variable costs. The variable costs can be calculated by multiplying the variable cost per program by the number of programs sold, so the variable cost is 3x.

Now let's set up the equation:

Total revenue = Total costs

5x = 1,400 + 3x

Next, subtract 3x from both sides of the equation:

2x = 1,400

Finally, divide both sides by 2 to solve for x:

x = 1,400 / 2

x = 700

So Byron would have to sell 700 programs to break even.

To calculate the number of programs Byron would have to sell to make a profit of $5,000, we can use a similar approach.

The profit can be calculated by subtracting the total costs from the total revenue.

Let's denote the number of programs Byron needs to sell as 'y'.

Total revenue = Total costs + Profit

The total revenue is again 5y.

The total costs include the fixed costs and the variable costs, which we already calculated as $1,400 + 3y.

So the equation becomes:

5y = (1,400 + 3y) + 5,000

Next, simplify the equation:

5y = 1,400 + 3y + 5,000

Combine like terms:

5y - 3y = 6,400

2y = 6,400

Finally, divide both sides by 2 to solve for y:

y = 6,400 / 2

y = 3,200

So Byron would have to sell 3,200 programs to make a profit of $5,000.