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Unformatted text preview: B1 Operations Operations Management Management Linear Programming Linear Programming Module B  Part 2 Module B  Part 2 B2 Problem B.23 Problem B.23 1. Gross Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. The profit from using each type of container is: $8 for each class A container, $6 for each class K container, and $14 for each class T container. The amount of packing material required by each A, K and T container is 2, 1 and 3 lbs., respectively. The amount of packing time required by each A, K, and T container is 2, 6, and 4 hours, respectively. There is 120 lbs of packing material available each week. Six packers must be employed full time (40 hours per week each). Determine how many containers to pack each week. B3 Problem B.23 Problem B.23 Container Profit Packing material (lbs.) Packing time (hrs.) A $8 2 1 Amount available K T $6 $14 3 2 6 4 ≤ 120 =240 B4 Problem B.23 Problem B.23 Maximize: 8x A + 6x K + 14x T 2x A + x K + 3x T ≤ 120 (lbs.) 2x A + 6x K + 4x T = 240 (hours) x A , x K , x T ≥ x i = Number of class i containers to pack each week. i=A, K, T B5 Linear Programming Solutions Linear Programming Solutions ♦ Unique Optimal Solution. ♦ Multiple Optimal Solutions. ♦ Infeasible (no solution). x + y ≤ 800 x ≥ 1000 x, y ≥ ♦ Unbounded (infinite solution). Maximize 3x + 2y x + y ≥ 1000 B6 Computer Solutions Computer Solutions ♦ Optimal values of decision variables and objective function. ♦ Sensitivity information for objective function coefficients. ♦ Sensitivity information for RHS (righthand side) of constraints and shadow price. B7 Computer Solutions Computer Solutions ♦ Enter data from formulation in Excel. ♦ 1 row for the coefficients of objective. ♦ 1 row for coefficients & RHS of each constraint. ♦ 1 final row for solution (decision variable) values. ♦ Select Solver from the Tools Menu. B8 Computer Solutions  Spreadsheet Computer Solutions  Spreadsheet B9 Computer Solutions  Spreadsheet Computer Solutions  Spreadsheet B10 Computer Solutions  Spreadsheet Computer Solutions  Spreadsheet B11 Computer Solutions  Solver Computer Solutions  Solver B12 Computer Solutions  Solver Computer Solutions  Solver B13 Computer Solutions  Solver Parameters Computer Solutions  Solver Parameters B14 Computer Solutions Computer Solutions ♦ Set Target Cell: to value of objective function. ♦ E3 ♦ Equal To: Max or Min ♦ By Changing Cells: = Sol’n values (decision variable values). ♦ B7:D7 ♦ Subject to the Constraints: ♦ Click Add to add each constraint: ♦ LHS =, ≤ , ≥ RHS B15 Computer Solutions  Adding Constraints Computer Solutions  Adding Constraints ♦ Cell Reference: LHS location ♦ Select sign : <=, =, >= ♦ Constraint: RHS location B16 Computer Solutions  Adding Constraints Computer Solutions  Adding Constraints ♦ 1st constraint....
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This note was uploaded on 02/15/2012 for the course BA 252 taught by Professor Jamescampbell during the Winter '03 term at UMSL.
 Winter '03
 JamesCampbell
 Management

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