An army wants to move troops from 3 training camps to 4 different bases. How should the troops be moved to minimize cost? Moving Cost Per Man Base 1 Base 2 Base 3 Base 4 Camp 1 \$34 \$26 \$29 \$31 Camp 2 \$42 \$33 \$28 \$35 Camp 3 \$36 \$29 \$32 \$38 Number Of Troops Moved Base 1 Base 2 Base 3 Base 4 Total Available Camp 1 100 100 100 100 400 500 Camp 2 100 100 100 100 400 400 Camp 3 100 100 100 100 400 400 Total 300 300 300 300 Required 200 250 350 300 Cost \$11,200 \$8,800 \$8,900 \$10,400 \$39,300 Problem An army wants to move troops from 3 training camps to 4 different bases. All costs of moving a soldier from any camp to any base are known. How should the army move the troops to minimize cost? Solution 1) The variables are the number of soldiers that are moved from each camp to each base. On worksheet Troops these are given the name Troops_moved. 2) The constraints are Troops_moved >= 0 via the Assume Non-Negative option Troops_per_camp <= Troops_available Troops_per_base = Troops_required 3) The objective is to minimize the total cost. This is defined on the worksheet as Total_cost. Remarks This model is a transportation model, like those shown in the Logistics Examples workbook. You might wonder why there is no constraint to assure that the numbers of troops moved are integers. It is a mathematical property of these types of problems that if the constants in the constraints are integers, the solution values for the variables are always integers. It is beyond the scope of these examples to further explore this.