Chapter 3, Problem 29RP

Explanation of Solution

Formulation of LP:

${\text{P}}_{\text{i}}$= Gallons of premium produced (and sold) during month $\text{i}$.

${\text{R}}_{\text{i}}$= Gallons of regular produced (and sold) during month $\text{i}$.

${\text{B}}_{\text{i}}$= Gallons of grade $\text{i}$ oranges bought for use during month 2.

${\text{I}}_{\text{j}}$= Gallons of grade $\text{j}$ oranges leftover at the end of month 1.

${\text{R}}_{\text{ij}}$= Gallons of grade $\text{j}$ oranges used to make regular juice during month $\text{i}$.

${\text{P}}_{\text{ij}}$= Gallons of grade $\text{j}$ oranges used to make premium juice during month $\text{i}$

Solution in LINDO is given below,

$\text{MAX 0}{\text{.9P}}_{\text{1}}\text{+0}{\text{.9P}}_{\text{2}}\text{+0}{\text{.7R}}_{\text{1}}\text{+0}{\text{.7R}}_{\text{2}}\text{-0}{\text{.4B}}_{\text{3}}\text{-0}{\text{.6B}}_{\text{6}}\text{-0}{\text{.05I}}_{\text{3}}\text{-0}{\text{.1I}}_{\text{6}}$

SUBJECT TO,

$\begin{array}{l}2) R_1-R_{16}-R_{13}= 0\\ 3) P_1-P_{13}-P_{16}= 0\\ 4) R_2-R_{26}-R_{23}= 0\\ 5) P_1-P_{13}-P_{16}= 0\end{array}$

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