Mathematics · Linear Programming
Consider 7 full bottles, 7 half-full, and 7 empty bottles of beverage. You want to divide these 21 bottles among 3 persons such that each receives 7 bottles and equal liquid quantity. When modeled as an Integer Linear Program to find a feasible assignment, what is the nature of the objective function and a feasible allocation?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Objective function uses binary decision variables: Person 1 gets (1 full, 2 half, 4 empty); Person 2 gets (5 full, 1 half, 1 empty); Person 3 gets (2 full, 2 half, 3 empty).
- 2Objective function minimizes empty bottles: Person 1 gets (0 full, 0 half, 7 empty); Person 2 gets (1 full, 1 half, 5 empty); Person 3 gets (2 full, 3 half, 2 empty).
- 3Objective function maximizes total bottles: Person 1 gets (3 full, 2 half, 2 empty); Person 2 gets (1 full, 1 half, 5 empty); Person 3 gets (2 full, 3 half, 1 empty).
- 4There will be a dummy objective function with all zero coefficients. Feasible allocation: Person 1 gets (1 full, 5 half, 1 empty); Persons 2 & 3 each get (3 full, 1 half, 3 empty).✓
Correct answer
There will be a dummy objective function with all zero coefficients. Feasible allocation: Person 1 gets (1 full, 5 half, 1 empty); Persons 2 & 3 each get (3 full, 1 half, 3 empty).
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