c = your cost
r = your revenue.
p = your profit.
c = 500 + 15x.
x is the number of items you made
r = 15y.
y is the number you sold.
most of these problems assume you sell what you make, so your revenue equation becomes:
r = 15x.
your profit is what you have left over after you sell your kites.
if your profit is negative, then it is a loss.
for example, a profit of -3 is a loss of 3.
your profit equation is p = r - c.
assuming you sell what you make, then:
r = 15 * x
c = 500 + 15 * x
p = r - c = 15 * x - (500 + 15 * x).
simplifying the profit equation, you get:
p = 15 * x - 500 - 15 * x.
simplify this equation to get p = -500.
assuming you sell what you make, your profit will always be -500 which is a loss of 500.
the only way you can hope to make a profit is if the sale price is more than the cost to make each item.
for example, assume r = 25 * x, rather than 15 * x.
the profit equation becomes:
p = 25 * x - (500 + 15 * x).
simplify this equation to get:
p = 25 * x - 500 + 15 * x.
simplify this equation to get:
p = 10 * x - 500.
now you can begin to make a profit after you sell 50 kites.
this is because p = 10 * 50 - 500 gets you p = 500 - 500 = 0.
that's your break even point.
sell less than 50 and you take a loss.
sell more than 50 and you make a profit.
to make a table, you would do something like this:
variable cost is 15 dollars for each unit made.
revenue is 15 dollars for each unit sold.
number of units made is assumed to be equal to number of units sold.
revenue is assumed to be variable only.
profit is equal to revenue minus fixed cost minus variable cost
number fixed cost variable cost revenue profit
0 500 0 0 -500
50 500 750 750 -500
100 500 1500 1500 -500
now assume revenue was 25 dollars per unit.
same table is used, except
variable cost is 15 dollars for each unit made.
revenue is 25 dollars for each unit sold.
number of units made is assumed to be equal to number of units sold.
revenue is assumed to be variable only.
profit is equal to revenue minus fixed cost minus variable cost
number fixed cost variable cost revenue profit
0 500 0 0 -500
50 500 750 1250 0
100 500 1500 2500 500