The Optimal Solution of the Linear Programming Problem Is at the Intersection

question 7

Essay

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.
Max
2x₁ + x₂
s.t.
4x₁ + 1x₂ $\le$ 400
4x₁ + 3x₂ $\le$ 600
1x₁ + 2x₂ $\le$ 300
x₁ , x₂ $\ge$ 0
a.Over what range can the coefficient of x₁ vary before the current solution is no longer optimal?
b.Over what range can the coefficient of x₂ vary before the current solution is no longer optimal?
c.Compute the dual prices for the three constraints.

---

Definitions:

CTU

In control systems, it typically stands for "Count Up", a function block used in PLC programming for counting events.

Count-Up Counter

A device or program that tallies an increasing count, often used for tracking occurrences or events.

Non-Retentive Counters

Counting mechanism in automation systems that do not retain their count value in the event of a power loss or system reset.

ACC

In the context of programmable logic controllers, ACC refers to the Accumulator, a register that holds interim arithmetic and logic results.