Linear Equation Worded Problem

The cost, *$C*, of manufacturing each jacket of a particular type is given by the formula

*C = an + b *for *0 < n ≤ 300*

where *a *and *b* are constants and *n* is the size of the production run of this type of jacket.

For making 100 jackets, the cost is $108 each.

For making 120 jackets, the cost is $100 each.

a) Find the values of *a* and *b*.

b) Sketch the graph of *C* against *n* for *0 < n ≤ 300. *

c) Find the cost of manufacturing each jacket if 200 jackets are made.

d) If the cost of manufacturing each jacket is $48.80, find the size of the production run.

If someone could point me in the right direction it would be much appreciated.

Re: Linear Equation Worded Problem

Hey Fratricide.

Please show us what you have tried and what you have thought about to solve the problem.

Re: Linear Equation Worded Problem

Initially I thought that I could substitute some values, so I did *108 = 100a + b* and tried solving for *a* and *b* but got hideously incorrect answers, and from there I have come to you.

Re: Linear Equation Worded Problem

Make the other equation for production of 120 jackets and get the values for a and b. thereafter everything will fall in its place.

Re: Linear Equation Worded Problem

Not quite sure I understand what you mean?

Re: Linear Equation Worded Problem

108 = 100a + b

100 = 120a + b

This will give a = -2/5 and b = 148

Re: Linear Equation Worded Problem

Thanks for your help. From there I was able to finish the question... mostly. The part of the question asking me to sketch the graph has me stumped. I thought I knew what I was doing, but then a wild 28 appeared! http://i.imgur.com/TElqRR7.jpg

Where does the 28 come from?

Re: Linear Equation Worded Problem

Re: Linear Equation Worded Problem

What appears to me is that he has just rtaken the production size to be 300 for the purpose of graph, though we can draw the graph in the absence of the point ( 300 , 28 )