Math word problem

[passionflower_40]

This is a problem that will challenge you to identify various factors that will influence the success of a multi-million dollar investment and suggest realistic mathematical approaches to achieving this company’s goal of maximizing its output. The intent is not for you to solve the problem, but to think about a mathematical approach to the problem. this problem have to do with systems of linear Equations and inequalities, the manufacturer wanted to know how many tables it could make from a given supply of lumber. This problem requires thinking about how that lumber might have been cut.



By the way, this is a real installation in a neighboring town. Since the installation of the new system the lumber company has seen a 15-18% increase in the yield of sawn lumber.





A local lumber company who supplies the table maker with sawn lumber wants to improve the effective use of the timber it buys. Logs arrive at the yard cut to a standard length, but the diameter of a given log may range from 6 inches to 24 inches. The bark is removed and used as fuel to heat the drying ovens. Peeled logs are sent to an automated mill and sawn into various size lumbers, trimmed to final dimensions, cured in drying ovens and shipped. The whole process “from stump to stud” takes four days.



The standard lumbers produced include 1 by 4’s, 1 by 6’s, 1 by 8’s, 1 by 12’s, 2 by 4’s, 2 by 6’s, 2 by 12’s, 4 by 4’s and 6 by 6’s. Any wood left over from the cutting is sent to a chipper and sold for very little profit.



The company naturally wants to get as many saleable board feet of high value sawn lumber from every log as it can. The salesman who wants to sell you a computer-controlled saw machine said it could be programmed to get the maximum amount of lumber from any log, regardless of diameter, automatically. This unit is the first saw machine in the process and rough-cuts trees into boards that will be trimmed to final dimension later. Your boss wants you to investigate these claims and tell him whether they make sense mathematically.



What are the mathematical approaches, factors, considerations and techniques that might make such a promise achievable? You may assume that a log’s diameter is constant (even though it isn’t, which makes the real solution even more complex!)

 

[ctelady]

Since the length does not matter, you could consider a cross-section in two-dimensions only. You essentially have circles of various diameters and you want to draw in specified sizes of rectangles to use up as much of the area as possible. You could work this out using chord lengths at various distances from the center to figure out how wide the circle is at each distance from the center. It sounds like the sort of thing that a computer could be programmed to calculate once the diameter is input.

 

[Denis]

Well I plopped down in my easy chair and turned on Channel Two

A bad gun slinger called Salty Sam was a chasin' poor Sweet Sue

He trapped her in the old sawmill and he said with an evil laugh

If you don't gimme the deed to your ranch I'll saw you all in half

And then he grabbed her (and then ?) he tied her up (and then ?)

He turned on the buzz saw (and then and then ?)

Eh eh and then along came Jones tall thin Jones

Slow walking Jones slow talking Jones along came long lean lanky Jones

 

[passionflower_40]

ctelady

Thank you. the diameters are 6 in., 12in., 18in. and 24in. I was thinking I had to find the board foot with mulitiplying the dimensions divided it by 12 to get the board foot. I guess I was wrong. thank you