Exam 7: Goal Programming and Multiple Objective Optimization

Exhibit 7.4 The following questions are based on the problem below. Robert Gardner runs a small, local-only delivery service. His fleet consists of three smaller panel trucks. He recently accepted a contract to deliver 12 shipping boxes of goods for delivery to 12 different customers. The box weights are: 210, 160, 320, 90, 110, 70, 410, 260, 170, 240, 80 and 180 for boxes 1 through 12, respectively. Since each truck differs each truck has different load capacities as given below: Robert would like each truck equally loaded, both in terms of number of boxes and in terms of total weight, while minimizing his shipping costs. Assume a cost of $50 per item for trucks carrying extra boxes and $0.10 per pound cost for trucks carrying less weight. The following integer goal programming formulation applies to his problem. Y₁ = weight loaded in truck 1; Y₂ = weight loaded in truck 2; Y₃ = weight loaded in truck 3; X_i,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. -Refer to Exhibit 7.4. Based on the integer goal programming formulation, the associated solution, and spreadsheet model, what formulas should go in cells B19:E19 and B24:E24 of the spreadsheet?

What is the soft constraint form of the following hard constraint? 3X₁ + 2 X₂ $\le$ 10