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Constraints
1) A constraint of the type ≤ (≥) can be converted to an equation by adding a slack variable to (subtracting a surplus variable form) the left side of the constraint.
For illustration, in the constraint: XI + 2X2 ≤ 6 we add a slack SI ≥ 0 to the left side to obtain the equation: XI + 2X2 + SI = 6, SI ≥ 0.
If the constraint represents the limit on the usage of a resource, SI will represent the slack or unused amount of the resource.
After that consider the constraint: 3XI + 2X2 - 3X3 ≥ 5, we subtract a surplus variable S2 ≥ 0 from the left side to obtain the equation.3XI + 2X2 - 3X3 - S2 = 5, S2 ≥ 02) The right side of an equation can always be made non-negative by multiplying both sides by -1.
For illustration, 2XI + 3X2 - 7X3 = -5 is mathematically equivalent to -2XI - 3X2 + 7X3 = +5.3) The direction of an equation is reversed when both sides are multiplied by -1. For illustration, whereas 2 < 4, -2 > -4. Thus the inequality 2XI - X2 ≤-5 can be replaced by -2XI + X2 ≥ 5.
During 2010, Jackson Company estimated that its manufacturing employees would work 80,000 direct labor hours. During the year the company actually worked 75,000 direct labor hours.
Ordering Costs These are incurred in getting purchased items into the company’s inventory or stores, and usually consist of clerical costs of: • Making the purchase demand.
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