MGMT 651_hw3_soln.docx - MGMT 651 u2013 Analytics for...

This preview shows page 1 - 4 out of 6 pages.

MGMT 651 – Analytics for Managerial Decision-Making Homework 3 SOLUTIONS Worth 100 points 1. (15 points) Chapter 4 Problem 1. a. Let T = number of television spot advertisements R = number of radio advertisements N = number of newspaper advertisements Max 100,000 T + 18,000 R + 40,000 N s.t. 2,000 T + 300 R + 600 N 18,200 Budget T 10 Max TV R 20 Max Radio N 10 Max News -0.5 T + 0.5 R - 0.5 N 0 Max 50% Radio 0.9 T - 0.1 R - 0.1 N 0 Min 10% TV T , R , N , 0 Budget $ Solution: T = 4 $8,000 R = 14 4,200 N = 10 6,000 $18,200 Audience = 1,052,000. The following solution is obtained: OPTIMAL SOLUTION Objective Function Value = 1052000.000 Variable Value Reduced Costs -------------- --------------- ------------------ T 4.000 0.000 R 14.000 0.000 N 10.000 0.000 b. The revised budget is $18,300. Re-solving the LP from part (a) with the budget constraint modified, the objective function value obtained is 1,057,130 (audience reached). Thus, a $100 increase in budget provides an increase in audience coverage of approximately 5,130. Submit your homework as one single attachment. Include Management Scientist/LINDO/POM-QM input and output screenshots wherever applicable. If you submit your homework in an MS-Excel document, make sure that it is properly formatted!! 1 of 6
2. (10 points) Chapter 4 Problem 6. Let x 1 = units of product 1 x 2 = units of product 2 Both product 1 and product 2 require 18 hours per unit of labor. Maximize 25x 1 + 20x 2 s.t. 18x 1 + 18x 2 ≤ 900 Hence produce 50 units of product 1 and none of product 2, using 300 hours in department A and 600 hours in department B, and producing a profit of $1,250. 3. (15 points) Chapter 4 Problem 8 Let x 1 = the number of officers scheduled to begin at 8:00 a.m. x 2 = the number of officers scheduled to begin at noon x 3 = the number of officers scheduled to begin at 4:00 p.m. x 4 = the number of officers scheduled to begin at 8:00 p.m. x 5 = the number of officers scheduled to begin at midnight x 6 = the number of officers scheduled to begin at 4:00 a.m. The objective function to minimize the number of officers required is as follows: Submit your homework as one single attachment. Include Management Scientist/LINDO/POM-QM input and output screenshots wherever applicable. If you submit your homework in an MS-Excel document, make sure that it is properly formatted!! 2 of 6
Min x 1 + x 2 + x 3 + x 4 + x 5 + x 6

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture