The Binding Constraints for This Problem Are the First and Second

question 33

Essay

The binding constraints for this problem are the first and second.
Min
x₁ + 2x₂
s.t.
x₁ + x₂ ≥ 300
2x₁ + x₂ ≥ 400
2x₁ + 5x₂ ≤ 750
x₁ , x₂ ≥ 0
a.Keeping c₂ fixed at 2, over what range can c₁ vary before there is a change in the optimal solution point?
b.Keeping c₁ fixed at 1, over what range can c₂ vary before there is a change in the optimal solution point?
c.If the objective function becomes Min 1.5x₁ + 2x₂, what will be the optimal values of x₁, x₂, and the objective function?
d.If the objective function becomes Min 7x₁ + 6x₂, what constraints will be binding?
e.Find the dual price for each constraint in the original problem.

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Definitions:

Double-Declining-Balance Method

A depreciation technique that accelerates the rate at which an asset loses value, doubling the rate of the straight-line depreciation method.

Straight-Line Method

A depreciation technique that allocates an equal amount of depreciation to each year of the asset's useful life.

Depreciation

The planned distribution of the costs associated with a tangible asset over its usage period.

Units-of-Activity Method

A depreciation method that allocates a fixed asset's cost based on its usage, activities, or units of production, reflecting wear and tear more accurately.