Home > Problem of the Week > Archive List > Detail

 << Prev 9/19/2010 Next >>

## Shame on Math Textbooks...Says Mother Nature

We wonder why our world is in such a sordid mess...foreign engagements, oil spills, power shortages, and sewage problems. But, then, consider these two problems from a mathematics textbook. Are we educating people to use mathematics to "avoid" laws?

[Problem 1, Exercise Set 8.2 B] The owner of an oil tanker must decide whether to install safety equipment aboard his ship at a cost of \$20,000. If he does not install the safety equipment and the ship develops an oil spill, his net profit will be \$500,000 after losses in oil and payments in fines are detected. If no oil spill develops, however, his net profit will be \$750,000. The probability of an oil spill without the equipment is 0.5 and with it is 0.

• Prepare a payoff matrix.
• Calculate the owner's maximum expected profit.
• Prepare a regret matrix.
• Calculate the owner's minimum loss of opportunity using the minimax principle.

[Problem 6, Exercise Set 8.1 B] Suppose a company calculates that it would cost \$10 million per month to maintain a treatment plane effective enough to keep the waste products it dumps into a river within legal cleanliness limits.
• If the chances of getting caught at a violation are 0.3 and the annual fine is \$100 million, is it in the short-term financial interests of the company to install the treatment plant?
• What is the minimum fine that would be a realistic deterrent?

Source: K. Kalmanson & P. Kenschott's Mathematics: A Practical Approach, 1978, pp. 355, 360

Hint: You can work through the problems if you want...but why? You are just learning how to use mathematics to evade the law!

Solution Commentary: One solution is to get rid of problems such as these from mathematics texts. As to other realistic solutions, that would require a extended debate (and endless legislation).