I got this in an e-mail from someone who was browsing this board but I don't think knew how to sign up to post it, and ended up e-mailing me about it. I'm not good at word problems :/
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!)
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!)
