![]() Example 3.27Īccording to U.S.postal regulations, the girth plus the length of a parcel sent by mail may not exceed 108 inches, where by girth we mean the perimeter of the smallest end. Initially, some substantial guidance is provided, but the problems progress to require greater independence as we move along. In this section the primary emphasis is on the reader solving problems. Upon establishing a function, we chose an appropriate domain and then were finally ready to apply the ideas of calculus to determine the absolute minimum or maximum. Instead, we first tried to understand the problem by drawing a figure and introducing variables, and then sought to develop a formula for a function that modeled the quantity to be optimized. Neither of these problems explicitly provided a function to optimize. Example3.26 subsequently investigated how the volume of a box constructed by removing squares from the corners of a piece of cardboard is dependent on the size of the squares removed. Example3.23 sought to maximize the total area enclosed by the combination of an equilateral triangle and a square built from a single piece of wire (cut in two). Near the conclusion of Section3.2, we considered two optimization problems in which determining the function to be optimized was part of the problem. In a setting where a situation is described for which optimal parameters are sought, how do we develop a function that models the situation and then use calculus to find the desired maximum or minimum? Section 3.3 Applied Optimization Motivating Questions
0 Comments
Leave a Reply. |