(Solution) IE 8520 Module 7 Assignment Spring 2017 Submit As Many Sheets As You Need! Put Answers That Require Discussion Into Excel Text Boxes. Question 1. A... | Snapessays.com

(Solution) IE 8520 Module 7 Assignment Spring 2017 Submit as many sheets as you need! Put answers that require discussion into Excel text boxes. Question 1. A...

I need help on setting up this linear program in excel.IE 8520

Spring 2017

Module 7 Assignment

Submit as many sheets as you need!

Put answers that require discussion into Excel text boxes.

And as

Question 1.

A TV crew wants to provide the right lighting for a show.

The zones for filming are divided

into nine blocks, and the amount of light (in units of “candelas”) required for each zone is shown below.

Zone 1, 1

Zone 1, 2

Zone 1, 3

Intensity = 600

Intensity = 800

Intensity = 400

Zone 2, 1

Zone 2, 2

Zone 2, 3

Intensity = 500

Intensity = 400

Intensity = 700

Zone 3, 1

Zone 3, 2

Zone 3, 3

Intensity = 1000

Intensity = 700

Intensity = 600

The stage can be lit using

three different types of lighting

, as described below.

?

Row beam:

A beam in row

i

provides light in zones (

i

, 1), (

i

, 2), and (

i

, 3), for any

i

= 1, 2, 3.

?

Column beam:

A beam in column

j

provides light in zones (1,

j

), (2,

j

), and (3,

j

), for any

j

= 1, 2, 3.

?

Spotlight beams:

These provide light only in a specific zone (

i

,

j

), for any

i

= 1, 2, 3 and

j

= 1, 2, 3.

Your goal is to determine the intensity of the 15 beams (3 horizontal, 3 vertical, 9 spotlight). They can all

be different intensities, so you will need 15 variables.

The intensities can be any nonnegative value,

including fractions.

The total amount of intensity in zone (

i

,

j

) is equal to:

(row

i

beam intensity) + (column

j

beam intensity) + (spotlight (

i

,

j

) beam intensity).

The company wants to minimize the intensity used by spotlight beams

.

Part a:

Suppose that the sum of light intensity that reaches a zone must perfectly equal the desired

intensity depicted in the table above.

Formulate a linear program

to minimize the sum of spotlight beam

intensities, subject to the restrictions that the stage must be lit exactly according to the table above.

Solve

this in Excel and describe your solution.

Part b:

Now, suppose that spotlights can no longer be used.

You will find that it is impossible to get the

right intensity in every zone using only row and column beams.

Formulate and solve (in Excel) a linear

program to provide a lighting plan that minimizes the largest absolute error in lighting for any zone

.

If that’s confusing, then here is an example.

Suppose that each row and column beam has an intensity of

300.

Then our (absolute) errors would be:

Zone 1, 1

Zone 1, 2

Zone 1, 3

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