Solved

The Following ILP Is Being Solved by the Branch and Bound

question 9

Essay

The following ILP is being solved by the branch and bound method. You have been given the initial relaxed IP solution. Complete the entries for the 3 nodes and label the arcs when you branch on X₁.
$\begin{array}{ll}\text { MAX: } & 35 \mathrm{X}_{1}+45 \mathrm{X}_{2} \\\text { Subject to: } & 35 \mathrm{X}_{1}+55 \mathrm{X}_{2} \leq 250 \\& 65 \mathrm{X}_{1}+25 \mathrm{X}_{2} \leq 340 \\& \mathrm{X}_{1}, \mathrm{X}_{2} \geq 0 \text { and integer }\end{array}$
Initial solution
X₁ = 4.6X₂ = 1.6
Obj = 233.9
$The following ILP is being solved by the branch and bound method. You have been given the initial relaxed IP solution. Complete the entries for the 3 nodes and label the arcs when you branch on X1. \begin{array}{ll} \text { MAX: } & 35 \mathrm{X}_{1}+45 \mathrm{X}_{2} \\ \text { Subject to: } & 35 \mathrm{X}_{1}+55 \mathrm{X}_{2} \leq 250 \\ & 65 \mathrm{X}_{1}+25 \mathrm{X}_{2} \leq 340 \\ & \mathrm{X}_{1}, \mathrm{X}_{2} \geq 0 \text { and integer } \end{array} Initial solution X1 = 4.6X2 = 1.6 Obj = 233.9$

Definitions:

Vein for IV Placement

A blood vessel suitable for the insertion of an intravenous line for medication delivery, fluid replacement, or blood sampling.

Dilated Vein

A vein that has expanded beyond its normal size, commonly due to increased blood flow or pressure.

Drops/Ml

A unit measurement commonly used in medicine and pharmacy to quantify liquid drugs, indicating the number of drops per milliliter.

D₅W

An abbreviation for a medical solution called Dextrose 5% in Water, a form of glucose solution used in intravenous therapy for nutrition and hydration.