A manufacturer has fixed costs of $5000 per week and variable cost of~X2 + 1 OX, where X is the number of tons produced; research has shown that, within the range of practicable prices, the relationship between price, P, and auantity X, is approximately P= 160-~X All production can be sold.

REQUIRED By examining the break-even position (or otherwise), advise the company of the production level at which it would be rational to operate.

ICMA, FS, Section B, Mathematics and Statistics, May 1982.