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Example Problem: A sales manager has 3 areas and 5 sales engineers.

Example Problem: A sales manager has 3 areas and 5 sales engineers. If the assignment of sales engineers to areas will result in the expected sales as shown, how should the engineers be assigned to maximize sales?. Sales (in $K) Area 1 Area 2 Area 3. 0 0 0 0

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Example Problem: A sales manager has 3 areas and 5 sales engineers.

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  1. Example Problem: A sales manager has 3 areas and 5 sales engineers. If the assignment of sales engineers to areas will result in the expected sales as shown, how should the engineers be assigned to maximize sales? Sales (in $K) Area 1 Area 2 Area 3 0 0 0 0 1 45 20 50 2 70 45 70 3 90 75 80 4 105 110 100 5 120 150 130 Number of Sales Engineers Assigned Stage 1 Stage 2 Stage 3

  2. Results Stage 1: x1 = 0 1 2 3 4 5 f1 (s1) x1 (s1) x1 * 0 1 2 3 4 5 s1 =

  3. Results Stage 2: x2 = 0 1 2 3 4 5 f2 (s2) x2 (s2) x2 * 0 1 2 3 4 5 s2 =

  4. Results Stage 3: x3 = 0 1 2 3 4 5 f3 (s3) x3 (s3) x3 * s3 = 5 Answer: x3 =1 s2 =s3 - x3 =4 x2 =3 s1 =s2 - x2 =1 x1 =1 f(x*) = f3 (s3) = 170 Assign 1 sales engineer to Area 3, 3 sales engineers to Area 2, and 1 sales engineer to Area 1. Total Sales = $170K

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