# M2.4.9

**inequalities**.

### Motivating Honest Budgets and Hard Work Simultaneously

Motivating honest budgets and profit expectations is difficult because some rnsubordinate managers will provide overly optimistic budgets to "look good" to rntheir bosses, while others will lowball budgets so they will "look good" when they rnexceed expectations. This paper explains how to motivate accurate forecasts of rnbudgets and profits.

### Isoperimetric Geometry

The isoperimetric theorem states that: "Among all shapes with an equal area, the circle will be characterized by the smallest perimeter" which is equivalent to "Among all shapes with equal perimeter, the circle will be characterized by the largest area." The theorem's name derives from three Greek words: 'isos' meaning 'same', 'peri' meaning 'around' and 'metron' meaning 'measure'. A perimeter (= 'peri' + 'metron') is the arc length along the boundary of a closed two-dimensional region (= a planar shape).