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HW3 solutions

# HW3 solutions - Problem318abcp.119 Decision Variables N1 =...

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Problem 3-18abc p. 119 N1 N2 N3 T1 T2 T3 Decision Variables 10 10 0 5 5 2 Objective Function 900 700 400 10000 7500 5000 113500 Budget 1000 900 800 12000 10000 8000 145000 Newspaper 1-10 1 10 Newspaper 11-20 1 10 Newspaper 21-30 1 0 TV 1-5 1 5 TV 6-10 1 5 TV 11-15 1 2 Newspaper 1-10 1 10 Newspaper 11-20 1 10 Newspaper 21-30 1 0 TV 1-5 1 5 TV 6-10 1 5 TV 11-15 1 2 Decision Variables: N1 = number of Newspaper ads to run at \$1,000 each N2 = number of Newspaper ads to run at \$900 each N3 = number of Newspaper ads to run at \$800 each T1 = number of Television ads to run at \$12,000 each T2 = number of Television ads to run at \$10,000 each T3 = number of Television ads to run at \$8,000 each Objective Function: MAX 900 N1 + 700 N2 + 400 N3 + 10,000 T1 + 7,500 T2 + 5,000 T3 Constraints: Budget: 1,000 N1 + 900 N2 + 800 N3 + 12,000 T1 + 10,000 T2 + 8,000 T3 ° 145,000 Newspaper Ads: N i 10 TV Ads: T i ° 5 Non-negativity: T i , N i > 0 The optimal solution is to run 20 newspaper ads and 12 TV ads, to reach the maxi

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<= 145000 <= 10 <= 10 <= 10 <= 5 <= 5 <= 5 >= 0 >= 0 >= 0 >= 0 >= 0 >= 0 imum number of customers (113500).

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Problem 3-20 p. 120 X1 X2 X3 X4 Decision Variables: 325000 162500 0 162500 Objective Function: 0.1 0.09 0.1 0.13 66625 Constraint 1 1 1 1 1 650000 <= 650000 Constraint 2 -0.25 -0.25 -0.25 0.75 0 <= 0 Constraint 3 0 -1 0 1 0 <= 0 Constraint 4 -1 0 0 1 -162500 <= 0 Constraint 5 1 325000 >= 0 Constraint 6 1 162500 >= 0 Constraint 7 1 0 >= 0 Constraint 8 1 162500 >= 0 Return =  10.250% Decision Variables: X1 = Amount invested in Bonds X2 = Amount invested in Mortgages X3 = Amount invested in Car loans X4 = Amount invested in Personal Loans Objective Function: MAX 10 X1 + 8.5 X2 + 9.5 X3 + 12.5 X4 Constraints: X1 + X2 + X3 + X4 <= 650,000 X4 .25*(X1 + X2 + X3 + X4 ) ==> -0.25X1 - 0.25X2 - 0.25X3 + 0.75X4 <= 0 X4 X2 ==> - 1X2 + 1X4 <= 0 X4 X1 ==>
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HW3 solutions - Problem318abcp.119 Decision Variables N1 =...

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