Cassimy_Evan_HOMEWORK 3 .docx.doc - Evan Cassimy MGMT 651...

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Evan Cassimy MGMT 651 1/26/2020 Professor Avijit Sarkar Homework 3 1. (20 points) Chapter 4 Problem 1* Part A Z = 100,000x 1 + 18,000x 2 + 40,000x 3 Budget Constraints: 2,000x 1 + 300x 2 + 600x 3 Minimum number of TV ads: x 1 > .10(x 1 + x 2 + x 3 ) .10x 2 + .10x 3 + - .90x 1 < 0 Maximum number of Radio ads: x 2 < .50(x 1 + x 2 + x 3 ) .50x 1 - .50x 2 + .50x 3 > 0 Maximum number of TV ads: x 1 < 10 Maximum number of radio ads: x 2 < 20 Maximum number of newspaper ads: X 3 < 10 Non-negativity constraints: x 1 > 0 x 2 > 0 x 3 > 0 Submit your homework as one single attachment. Include POM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! 1 of 11
Number of tv ads to be run = 4 Number of radio ads to be run = 14 Number of newspaper ads to be run = 10 Allocated tv ad budget = $8,000 Allocated radio ad budget = $4,200 Allocated newspaper budget = $6,000 Total audience reacehd = 1,052,000 Submit your homework as one single attachment. Include POM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! 2 of 11
Part B Z = 100,000x 1 + 18,000x 2 + 40,000x 3 Budget Constraints: 2,000x 1 + 300x 2 + 600x 3 < 18,300 Minimum number of TV ads: x 1 > .10(x 1 + x 2 + x 3 ) .10x 2 + .10x 3 + - 0.90x 1 < 0 Maximum number of Radio ads: x 2 < .50(x 1 + x 2 + x 3 ) .50x 1 - .50x 2 + .50x 3 > 0 Maximum number of TV ads: x 1 < 10 Maximum number of radio ads: x 2 < 20 Maximum number of newspaper ads: X 3 < 10 Non-negativity constraints: x 1 > 0 x 2 > 0 x 3 > 0 Total audience reached = 1,057,130 Audience contact increase = 5,130 when an extra $100 is allocated to the promotional budget. 2. (15 points) Chapter 4 Problem 8. Submit your homework as one single attachment. Include POM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! 3 of 11
Consider X 1 = number of officers beginning work from 8:00 AM – Noon X 2 = number of officers beginning work from Noon – 4:00 PM X 3 = number of officers beginning work from 4:00 PM – 8:00 PM X 4 = number of officers beginning work from 8:00 – Midnight X 5 = number of officers beginning work from Midnight – 4:00 AM X 6 = number of officers beginning work from 4:00 AM – 8:00 AM Objective function Minimize Z = X 1 + X 2 + X 3 + X 4 + X 5 + X 6 Subject to constraints X 6 + X 1 > 5 X 1 + X 2 > 6 X 2 + X 3 > 10 X 3 + X 4 > 7 X 4 + X 5 > 4 X 5 + X 6 > 6 Restriction Variable X 1 , X 2 , X 3 , X 4 , X 5 , X 6 > 0 Submit your homework as one single attachment. Include POM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! 4 of 11

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