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) Graph the cost equation.
(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.
(d) How many items must be produced for the revenue to equal the cost (the
break-even point)?
what is your question? a) is just plug the numbers in for m,b. b) is graph it.
c) is graph a new equation on the same graph.
d) is where the lines cross.
You will have to draw your own graphs. We can't do it for you here.
(a) Cost: C = 10 x + 40 (in dollars)
(c) Revenue: R = 50 x
(d) Look for the point on your graph were the C and R lines intersect. That will be the breakeven point.
It will also be where 10 x + 40 = 50 x
To solve equation (d) for the break-even point, we need to find the value of x where the cost and revenue are equal.
Setting the cost equation (C = 10x + 40) equal to the revenue equation (R = 50x), we have:
10x + 40 = 50x
To solve for x, we can begin by subtracting 10x from both sides of the equation:
40 = 40x
Now, divide both sides of the equation by 40:
x = 1
Therefore, 1 item must be produced for the revenue to equal the cost, which is the break-even point.