Chapter 3, Problem 38RP

Explanation of Solution

LP to minimize the cost of obtaining monthly demands:

• Let “${\text{A}}_{\text{pq}}$” be the units of product “p” made on equipment “q”.
• The Linear Programming (LP) to minimize the cost of achieving monthly demands is as follows,

  $\text{min z=1}{\text{.5A}}_{\text{11}}\text{+0}{\text{.4A}}_{21}\text{+2}{\text{.2A}}_{\text{12}}{\text{+4A}}_{22}$

  $\begin{array}{l}\text{S}\text{.T}\\ \text{0}{\text{.7A}}_{\text{11}}\text{+0}{\text{.75A}}_{\text{21}}\le \text{200}\text{(Time}\text{constraint}\text{on}\text{Machine"1")}\\ 0.75{\text{A}}_{\text{21}}+0.75{\text{A}}_{\text{22}}\le 200\text{(Time}\text{constraint}\text{on}\text{Machine"2")}\\ \text{0}{\text{.75A}}_{\text{11}}\text{+0}{\text{.75A}}_{\text{21}}+1\end{array}$