Functions!!

[chutch82]

A company producing DVD players has fixed costs of $400 per day and total costs of $800 at a daily output of 40 players. If the total cost function C depends linearly on the daily output of x players, what will the total daily costs of producing 55 players?

I'm not really sure how to even approach this problem! thanks!

 

[mmm4444bot]

You've already learned the linear relationship between x and y:

y = mx + b

This is a function; x is the input and y is the output.

In your exercise, they've changed the name of y to C:

C = mx + b

And, if you understand function notation for y, you can write instead:

C(x) = mx + b

So far, we have four symbolic numbers: C(x), m, x, and b. The exercise gives you three of these four numbers; so, you need to first find the value of the fourth number, and then you can use the function to answer the question.

A company producing DVD players has fixed costs of $400 per day and total daily costs of $800, at a daily output of 40 DVD players.

The symbol C(x) represents "total daily cost"

The symbol x represents "daily output of DVD players"

The symbol b represents "fixed costs per day"

Substitute the three given numbers for the symbols above into C(x) = mx + b, and solve for m.

Once you know m, you can answer the question. They want to know the value of C(55).

Please show your work, or ask specific questions about parts that you do not understand, if you still need help.

Cheers ~ Mark :cool:

 

[chutch82]

math

i think i might be switching the numbers around wrong.

800(40)=m(40)+400
m=790

 

[mmm4444bot]

No, I don't think that's your issue.

Your issue is that you do not yet understand function notation.

The notation C(x) is a single symbol (composed of four characters) that represents the function output. "C" is the name of the function. The symbol C(x) is not an expression that means C times x.

So, let's skip function notation for now and simply use symbol C to represent both the name of the function and its output. Later on, you'll come to realize the benefits of writing C(x) instead of C.

C = mx + b

Now, try again.

 

[chutch82]

800=m(40)+400
m=10

 

[mmm4444bot]

That's correct.

Now that you know the values of m and b, you can write the actual function definition for C:

C = mx + b

After you substitute your values for m and b above, they want you to figure out what C is when x is 55.

 

[chutch82]

C=10(55)+400
C=950

Thank you so much for all your help. I really appreciate it!