University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2019
Views:

455

Pages:

4
Author:

Clint W.

CALCULUS 0PTIMIZATION N0TES ASSIGNMENT: 0ptimization Web Assign 8ectives: • Solve applied minimum and maximum proЫems. Minimum and Maximum Applications One of the most common applications of calculus involves the determination of minimum and maximum values. Consider how frequently you hear or read terms such as greatest profit, least cost, least time, greatest voltage, optimum size, least size, greatest strength, and greatest distance. Example 1: А manufacturer wants to design an open Ьох having а square base and а surface area of 108 square inches, as shown in Figure 3.46. What dimensions will produce а Ьох with maximum -==volume? • e;Q �C>Q.. ьu,мg. &'1,.:. = \�� ===-> цs� �00> 1 н 'i1-( 10� oU)iv.6 ::: x-z. h \А) .r \,S �u6 м �"' S ::::. i- -'-4№::.: 1 о-& е.� . Open ьох With square ьаsе: ?. ::: 7-1-х- {° х � tлs� l�т �,-&S, '3, - s = х2 + 4xh = 108 Figure З.46 2� --¾х2. ! f�;,;:\ ь , х� (i,:�- (\мА'/.. 1, 1-s д. ��у. l�е>-з,.,._ 2 \ _ I -f-:.1 / t о� atь-� t= ,>ffi --;;;;,, / • AJJf) \-\:::: Чх �, ln Example 1, you should realize that there are infinitely many open boxes having 108 square inches of surface area. То begin solving the proЫem, you might ask yourself which basic shape would seem to yield а maximum volume. Should the Ьох Ье tall, squat, or nearly cublcal? Wlllcn ьох nas tne greatest votume? . 8х8х t� Remember that you are not ready to begin solving а proЫem until you have clearly identified what the proЫem is.