Question 623556
x = number of units produced.
cost per unit = 29.8
revenue per unit = 34
fixed cost = 200
C = Total Cost
R = Total Revenue
C = 200 + 29.8*x
R = 34*x
P = R - C
P = 34*x - 29.8*x - 200
P = 4.2*x - 200
You don't get a profit until P is greater than or equal to 0.
You can graph these equations.
Revenue equation would be y = 34*x
Cost equation would be y = 29.8*x + 200
Profit equation would be y = 4.2*x - 200
Each will be graphed separately below:
cost equation is:
{{{graph(600,600,-10,100,-5,3500,200+29.8*x)}}}
revenue equation is:
{{{graph(600,600,-10,100,-5,3500,34*x)}}}
profit equation is:
{{{graph(600,600,-10,100,-205,350,4.2*x-200)}}}
the graphs suggest a break even point at somewhere betweeen 45 and 50.
calculation of the break even point is shown below:
this is the point where the revenue equals the cost.
you get R = C which becomes:
34*x =  29.8*x + 200
subtract 29.8*x from both sides of this equation to get:
34*x - 29.8*x = 200
simplify to get:
4.20 * x  = 200
divide both sides by 4.20 to get:
x =  200 / 4.2 = 47.61904762
that's your break even point.
this happens when revenue is equal to 34 * 47.61904762 = 1619.047619.
this happens when cost is equal to 29.8 * 47.61904762 + 200 = 1619.047619.
that actual break even point is easier to see if you graph the revenue and cost equations together as shown below:
{{{graph(600,600,-10,100,-5,3500,200+29.8*x,34*x,1619.04)}}}
a horizontal line at 1619.04 assists you.