(a) A project management consultant estimated that if a particular project was completed, t years after completion, N thousand persons would benefit directly from the project, where t3 N(t) ==- 4.5t2 + 16t, %3D 0

(a) A project management consultant estimated that if a particular project was completed, t years after completion, N thousand persons would benefit directly from the project, where t3 N(t) ==- 4.5t2 + 16t, %3D 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5T

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

(a) A project management consultant estimated that if a particular project was
completed, t years after completion, N thousand persons would benefit directly from
the project, where
t3
N(t)
==-
4.5t2 + 16t,
%3D
0<t< 10
|
3
For what value of t, will the largest number of people receive direct benefits?
(b) A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires
20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packaging
time. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and
12 minutes of packaging time. Each blouse requires 10 minutes of cutting time,
24 minutes of sewing time and 6 minutes of packaging time.
The amount of time available for cutting, sewing and packaging is 115 hours,
280 hours and 65 hours respectively. Using either the Inverse Method or the
Cramer's Rule, determine how many of each type of clothing should be made
to use all available labour hours?
7.

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