another one that I need help.....word problem

[smelius]

The manager of a furniture factory finds that it costs $2200 dollars to manufacture 100 chairs in one day and $4800 to manufacture 300 chairs in one day.

a) Assuming the relationship between cost and the number of chairs produced is linear, find an equation that expresses cost as a function of the number of chairs manufactured

b) What are the units of slope?

c) Interpret the slope in terms of the two variables.....


Anyone please help me to start this off :?:

 

[dagr8est]

a)
Let y=total cost
Let x=total number of chairs

Then y=mx+b is the linear function where m=cost per chair, and b=cost of running factory.

2200=100m+b
4800=300m+b

Then 2200-100m=4800-300m

1. Solve for m
2. You now know y, m, and x, so solve for b
3. Plug in m and b into y=mx+b and you will have the general function

b)
m is the slope. What does m represent?

c)
I'm not sure what this question is asking... You're on your own.

 

[Matt]

c) Interpret the slope in terms of the two variables.....

c)
I'm not sure what this question is asking... You're on your own.

Maybe the answer is supposed to be something like "if the factory manufactures 100 more chairs per day, then the cost will increase by ___ dollars."

 

[tkhunny]

The slope is negative. This makes the unit cost of a chair DEcrease as the number of chairs produced INcreases. The more you crank out, the cheaper it is to produce them.

P.S. Presumably, there would be a limit to this. The cost CAN'T go down all the way to zero.

 

[Matt]

The slope is negative.

No, the slope is positive.

. . . .

Both points (100, 2200) and (300, 4800) were given in the problem.

This makes the unit cost of chairs DEcrease as the number of chairs produced INcreases. The more you crank out, the cheaper it is to produce them.

The y-values represent the total cost for x chairs, not the unit cost per chair.

 

[smelius]

thanks guys..... :wink:

 

[tkhunny]

No, the slope is positive.

Yikes! Well, I guess that's what I get for looking at only half the equation.

Smelius,
Forget I said anything. Listen to Matt, on this one.

I see why folks were having trouble interpreting the slope, since it is horribly obvious that the cost of making chairs would go up with the number of chairs made. That must have been why I got so excited over SOME interpretation of my fake negative slope. The UNIT cost, would be the same equation divided by x and would demonstrate clearly the diminishing marginal cost I was talking about, but that's a lesson for another day.

"Smelius" Is this a tribute to a famous Finnish composer?