Chapter 3, Problem 43QP

a)

Summary Introduction

Toformulate: A linear programming model for the problem.

Explanation of Solution

Formulation:

$\begin{array}{c}\text{Minimize}=A_{12}+B_{13}+C_{14}+D_{18}\\ \text{Subject to:}\\ 1.06A_{12}-A_{23}=0\\ 1.06A_{23}+1.14B_{13}-A_{34}-B_{35}=0\\ 1.06A_{34}+1.18C_{14}-A_{45}-C_{47}=0\\ 1.06A_{45}+1.14B_5-A_{56}-B_{57}=0\\ 1.06A_{56}-A_7=12\\ 1.06A_{67}+1.14B_{57}+1.18C_{47}-A_{78}-B_{79}=14\\ 1.06A_{78}+1.65D_{18}-A_{89}=16\\ 1.06A_{89}+1.14B_{79}=18\\ -3A_{12}-B_{13}+2C_{14}+4D_{18}\le 0\\ -3A_{23}-B_{13}+2C_{14}+4D_{18}\le 0\\ -3A_{34}-B_{35}+2C_{14}+4D_{18}\le 0\\ -3A_{45}-B_{35}+2C_{47}+4D_{18}\le 0\\ -3A_{45}-B_{35}+2C_{47}+4D_{18}\le 0\\ -3A_{56}-B_{57}+2C_{47}+4D_{18}\le 0\\ -3A_{67}-B_{57}+2C_{47}+4D_{18}\le 0\\ -3A_{78}-B_{79}+4D_{18}\le 0\\ -3A_{89}-B_{79}\le 0\\ A_{ij},B_{ij},C_{ij},D_{ij}\ge 0\end{array}$

b)

Summary Introduction

Todevelop: A spreadsheet model and solve using solver.

Explanation of Solution

Model:

Formulae:

Solver input:

Answer:

c)

Summary Introduction

Toidentify: The optimal solution.

Explanation of Solution

Optimal solution: