(a) A project management consultant estimated that if a particular project wascompleted, t years after completion, N thousand persons would benefit directly fromthe project, whereN(t)4.5t2 + 16t,30st< 10For what value of t,will the largest number of people receive direct benefits?(b) A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packagingtime. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and12 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 theCramer's Rule, determine how many of each type of clothing should be madeto use all available labour hours?

Name: (a) A project management consultant estimated that if a particular pr
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Description: (a) A project management consultant estimated that if a particular project wascompleted, t years after completion, N thousand persons would benefit directly fromthe project, whereN(t)4.5t2 + 16t,30st< 10For what value of t,will the largest number of

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(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
N(t)
4.5t2 + 16t,
3
0st< 10
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?

Expert Solution

Step 1

According to the given information,

A project management estimate that if a particular project was completed, t years after completion, N thousands persons would benefit directly from the project where N(t) is denoted by:

It is required to calculate the value of t will the largest number of people receive direct benefits.

Step 2

Use second derivative test to find the value of t.

Step 3

Now since t is in the closed interval [0,10] so,

Step 4

Now for part (b)

Let, x be the number of trousers made

Y be the number of skirts made

And, z be the number of blouse made.

So, according to question the equations formed are:

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