What Is the Interpretation of the Slope in This Word Problem?

[salma17]

Use the following situation to answer questions 10 and 11.
A toy manufacturer determines that it will cost $8,000 to produce 500 dolls a week and $14,000 to produce 1000 dolls a week.

10) Express the cost, C, as a function of the number of dolls produced, x, assuming that it is linear.
a)C = 12x + 8000
b)C = 12x - 2000
c)C = 12x + 2000
d)C = ½x - 3500
e)C = ½x + 3500

11) Which of the following statements is the best interpretation of the slope in problem
number 10?
a) The amount the company charges for each doll.
b) The amount it costs the company to produce each doll.
c) The amount of profit the company receives for each doll.
d) The amount the company’s costs are increasing each year.
e) The amount the company’s profits are increasing for each year.

For 10, I got C because I basically went through each choice and plugged in the numbers to see which would satisfy both. So c) which is C=12x+2000 satisfies both because 12(500)+2000 is 8000. and 12(1000)+2000 is 14000.

Im not sure about 11 though. I am thinking about B, or maybe A.not sure. Can anyone help me with this one please?

 

[berkeman]

Use the following situation to answer questions 10 and 11.
A toy manufacturer determines that it will cost $8,000 to produce 500 dolls a week and $14,000 to produce 1000 dolls a week.

10) Express the cost, C, as a function of the number of dolls produced, x, assuming that it is linear.
a)C = 12x + 8000
b)C = 12x - 2000
c)C = 12x + 2000
d)C = ½x - 3500
e)C = ½x + 3500

11) Which of the following statements is the best interpretation of the slope in problem
number 10?
a) The amount the company charges for each doll.
b) The amount it costs the company to produce each doll.
c) The amount of profit the company receives for each doll.
d) The amount the company’s costs are increasing each year.
e) The amount the company’s profits are increasing for each year.

For 10, I got C because I basically went through each choice and plugged in the numbers to see which would satisfy both. So c) which is C=12x+2000 satisfies both because 12(500)+2000 is 8000. and 12(1000)+2000 is 14000.

Im not sure about 11 though. I am thinking about B, or maybe A.not sure. Can anyone help me with this one please?

Don't just use the "plug in and check" method on these problems. You should make a graph for the first problem, and that will help you answer the 2nd problem.

Make your graph with the number of dolls on the x axis, and the total cost on the vertical axis. Use that to re-check your first answer (which is correct), and now tell us how you can use the graph to answer the 2nd question.

 

[salma17]

Ok, I attached what my graph looks like. I immediately eliminated choices D and E because the question doesn't say anything is increasing. I am actually not sure how the graph can help me with #11 though. Can i have a hint :)

 

[berkeman]

Ok, I attached what my graph looks like. I immediately eliminated choices D and E because the question doesn't say anything is increasing. I am actually not sure how the graph can help me with #11 though. Can i have a hint :)

The graph looks wrong. The axes need labels with tick marks to show amounts, and the line must pass through the two datapoints listed in the problem statement.

 

[salma17]

Ive attached my graph. does this one look right?

 

[berkeman]

Ive attached my graph. does this one look right?

That's closer, but it would be better if the x and y axes crossed at the point (0,0). Especially for y = mx + b type of linear plots, interpretation of the line is much easier if the plot's origin is (0,0).

Make that change, and you should be able to answer the 2nd question now...

 

[salma17]

Ok, I really think its B. i don't think the other options are represented by the graph i made.

 

[berkeman]

Ok, I really think its B. i don't think the other options are represented by the graph i made.

I agree. Good job.

 

[salma17]

thanks for your help