How to Identify Constraints in Linear Programming
- 1). Read the word problem entirely to become familiarized with the content. Read through again and highlight any numbers. Explicitly stated numbers may either be a coefficient in the expression or a constraint.
- 2). Identify the end-goal of the problem. In linear programming, the end-goal is the value to be minimized or maximized. Some common adjectives to look for include "highest," "lowest," "most" or "least."
- 3). Identify the decision variables of the problem. The decision variables (x, y, z) are the modifiable values in the problem and will affect the end goal. For example, in a profit maximization problem that states, "each burger sold nets $1.00 profit and each milkshake nets $0.50 profit," then the decision variables would be the number of burgers sold and number of milkshakes sold.
- 4). Locate words that equate to inequalities. Words like "at least," "at most," "minimum," "maximum," "more than" or "less than" can be converted into inequalities based on what is being compared. These inequalities are the rough forms of the linear programming problem's constraints. The words should be describing one or more of the decision variables. For example, the statement "at least as many apples as bananas" would produce an inequality of "a >= b" where "a" is the number of apples and "b" is the number of bananas.
- 5). Rearrange the inequalities so all variables are on one side of the expression. The expression "a >= b" would become "a -- b >= 0." This is the standard format for linear programming constraints.
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