In the rectangle problem, a feasible alternative must satisfy the condition w + h = with wand h assuming nonnegative values. This leads to an infinite number of feasible solutions and, unlike
the tickets problem, the optimum solution is determined by an appropriate mathemat- ical tool (in this case, differential calculus).
Question: In the rectangle problem, identify two feasible solutions and determine which one is better?
Sider forming a maximum-area rectangle out of a piece of wire of length L inches. What should be the width and height of the rectangle? In contrast with the tickets example, the number of alternatives in the present ex- ample is not finite; namely, the width and height of the rectangle can assume an infinite number of values. To fornalize this observation, the alternatives of the problem are identified by defining the width and height as continuous (algebraic) variables. Let w-width of the rectangle in inches h = height of the rectangle in inches Based on these definitions, the restrictions of the situation can be expressed verbally as 1. Width of rectangle + Height of rectangle – Half the length of the wire 2. Width and height cannot be negative These restrictions are translated algebraically as