Question 60915
The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item).
(a) If the fixed cost is $40 and the variable cost is $10, write the cost equation.
b=40, m=10
{{{highlight(C=10x+40)}}}
(b) Graph the cost equation.
{{{graph(300,200,-10,10,-10,50,10x+40)}}}
(c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation.
{{{graph(300,200,-10,10,-10,60,10x+40,50x)}}}
(d) How many items must be produced for the revenue to equal the cost (the break-even point)?  The lines intersect at (1,50), therefore the number of items that must be produced to break even is x=1.
You could have found this algebraically by letting C=R
10x+40=50x
10x-10x+40=50x-10x
40=40x
40/40=40x/40
1=x
Happy Calculating!!!