Please help with this problem.?

Question

A company can produce 100 candy bars for 150 dollars and 600 candy bars for 200 dollars. Find the cost function and determine the fixed cost and the variable cost per candy bar

Answer 1

Assuming the relationship is LINEAR, the above answers should be right.

Answer 2

There is a fixed cost 'f' (for the machine, which you buy once) + a variable cost 'v' (for the chocolate, which you buy for every bar.) We can translate the English into Math, like this.

The total cost we'll call 't', which is equal to the machine, plus the cost of 1 candy bar x the # of candy bars we want, which I'll call 'b'. Or...

t = f + vb

"A company can produce 100 candy bars for 150 dollars"
150 = f + v(100) (equation #1)

"and 600 candy bars for 200 dollars"
200 = f + v(600) (equation #2)

So, we have two equations, with two unknowns. I'm not sure how you've been taught to solve these, but I'm going to use the addition/subtraction method.

Equation #2 - Equation #1 = ...

200 - 150 = (f + 600v) - (f + 100v)
50 = 500v [How did I do this?]
0.10 = v. So the cost for one candy bar is $0.10. Not bad! But what about the machine?

Ok, Ok. Let's go back to Equation 1, although the other one would work just fine...

150 = f + v(100) [But wait! You know what V is!]
150 = f + (0.10)(100) [Yeah, now this is easy!]
150 = f + 10
140 = f [Why?]

[So how do I know this really works??]

Give it a try in equation #2.
[You mean...]
Yep, start with 200 = f + v(600), but plug in f and v, because your checking to see if they are right...

Answer 3

Im assuming the cost function is linear.

Let c = # candy bars
y = f(x) = cost to make it

Then (100,150) and (600,200) are points on the line.

y - 150 = (200-150)/(600-100) * (x - 100)

y = 150 + 50 / 500 * (x - 100) = 200 + 1/10 * x -10
y = 140 + 1/10 * x

Thus the fixed cost is 140 (The y intercept)

The variable cost (the slope) is 1/10th of a dollar or $0.10 dollars per candy bar.

Answer 4

Okey doke. No biggie. Our two points are:

x1=100, y1=150
x2=600, y2=200

simple formlua for the slope of the line between two points:

(y2-y1)/(x2-x1)

Plugging in the values you get that the slope, in this case your MC = 1/10

Fixed cost is simply the y-intercept (recall the definition of fixed cost). So solve the following equation

150 = 1/10(100)+FC

So your FC = 140, and thus your cost function is

C(x) = 1/10*x+140

Regarding variable cost. In reality, "what is the the variable cost per candy bar really doesn't make any sense. You can ask what the variable cost is at x bars, what the average variable cost is, or the total variable cost is for a given output - per bar is somewhat meaningless. But here, I think for your purposes, simply using the MC should be fine).

Answer 5

It's just a slope, y intercept problem.
Find the equation of the line going through the points (100,150) and (600, 200).
The fixed cost is just the y intercept and the cost per bar is the slope.