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mathstudy

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discrete mathematics problem

I am studying discrete mathematics from the book Discrete Mathematics 5th Edition by Dossey, Otto, Spence, Vanden Eynden.  I am on the 1st chapter and have completed a number of problems successfully, but I ran into one today that I cannot seem to figure out.  My answer does not match the one in the book.  This has to do with critical path analysis.  This particular one gives a story and it seems you would apply the technique the chapter has covered thus far.  Here is the problem: #17 in section 1.1 exercises...."A small purse manufacturer has a single machine that makes the metal parts of a purse.  This takes 2 minutes.  Another single machine makes the cloth parts in 3 minutes.  Then it takes a worker 4 minutes to sew the cloth and metal parts together.  Only one worker has the skill to do this.  How long will it take to make 6 purses?"  I came up with 42 minutes, but the answer shown in the book is 27 minutes.  This seems like such a simple one, but I must be doing something incorrectly.  If you know the diagram I should be forming and using, please share.  Thank you!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: discrete mathematics problem

Hi;

I like 27 minutes too.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: discrete mathematics problem

hi mathstudy

Welcome to the forum.

I see where you are getting 42 from.  One purse takes 3 + 4 = 7.  Then multiply by 6.

But while the first purse is being sewn the cloth for the second can be made, thereby saving time.  By the time the first is fully made the cloth is ready for the second.

This can continue throughout, making the critical path 3 + 4 + 4 + 4 + 4 + 4 + 4 = 3 + 24 = 27.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob