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)?
A) Did
x=0
y=40
x=10
y=140
B) i put the points in the graph
(0,40) (0,140)
C) now this is my problem
do i replace the x with
R=50*0 then solve and then
R=50*10 and then solve and put those points in also and draw a trend line if i am missing some thing i am not sure where
D) I have figured out how to solve this part I am hoping it will solve once i get the right equations in the graph please help
a)
If the fixed cost is $40 and the variable cost is $10 then the cost of:
1 item is $10 + $40 =$50
2 items is $20 + $40=$60
10 items is $100+ $40 = $140
20 items is $200 + $40=$240
x items is $10x + $40 = y (where y is the total cost)
"B) i put the points in the graph
(0,40) (0,140)" No, I think you can see that the second point is not right from a)
To plot R=50x (plot R on the y axis)
so if x=0, R=0
and if x=20, R=1000
If you plot the two lines, where they cross is the break even point.
Hope this helps.
if you don't want to find the break even point graphically (i wouldnt recommend using a graph becuase you MIGHT make a mistake on the graph, which would affect your answer to the break-even)..Personally, I hate graphs. I find equations simpler and more reliable.
Break-even is the point where Revenue=Cost
R=C
So, 50X=10X+40
Get all your X's on one side, so you have to throw the 10X over to the left
50X-10X=40
40X=40
So, X=1.
so x=1. and the cost is c=10x+40, and the revenue is r=50x.
then the total cost must be 50 and the revenue is 50. they are even.
this didn't help at all.
i needed help with breaking points not graphing.
Great job! You correctly found the cost equation in part (a) by adding the fixed cost and the variable cost. The cost equation is C = 10x + 40, where C represents the total cost of producing x items.
In part (b), you mentioned putting the points (0, 40) and (0, 140) on the graph. However, the second point should be (10, 140) instead, as you calculated correctly that producing 10 items would cost $140. It seems you made a typo in your explanation, but you had the correct points in your subsequent response.
For part (c), to graph the revenue equation R = 50x, you need to plot points (x, R). Since revenue is directly proportional to the number of items produced, if x is 0, the revenue will also be 0. And if x is 20, the revenue would be 50 * 20 = 1000. So the two points you can plot are (0, 0) and (20, 1000). On the same graph, you can plot the cost equation by using the points you calculated in part (a), such as (0, 40) and (10, 140).
To find the break-even point in part (d), you correctly set the revenue equation equal to the cost equation: 50x = 10x + 40. By simplifying and solving for x, you found that x equals 1. This means that the break-even point occurs when 1 item is produced. You can substitute this value back into the cost or revenue equation to find the corresponding cost or revenue at the break-even point.
To summarize:
(a) The cost equation is C = 10x + 40
(b) Plot the cost equation by using the points (0, 40) and (10, 140), and plot the revenue equation R = 50x using the points (0, 0) and (20, 1000).
(c) Plot both equations on the same graph.
(d) The break-even point occurs when x = 1, and at that point, the cost and revenue will both equal $50.