Chapter 3, Problem 16RP

Explanation of Solution

Modified formulation:

• The old formulation is as follows,

  $\text{min z = 1000}\left({\text{x}}_{\text{1}}{\text{+x}}_{\text{2}}{\text{+x}}_{\text{3}}{\text{+x}}_{\text{4}}{\text{+x}}_{\text{5}}\right)\text{+2000}\left({\text{y}}_{\text{1}}{\text{+y}}_{\text{2}}{\text{+y}}_{\text{3}}{\text{+y}}_{\text{4}}{\text{+y}}_{\text{5}}\right)$

• The above function subject to the following constraints,

  $\begin{array}{l}\begin{array}{l}{\text{160y}}_{\text{1}}-{\text{50x}}_{\text{1}}\ge \text{6,000 }\left(\text{January Constraint}\right)\\ {\text{160y}}_{\text{2}}-{\text{50x}}_{\text{2}}\ge \text{7,000 }\left(\text{February Constraint}\right)\end{array}\hfill \\ {\text{160y}}_{\text{3}}-{\text{ 50x}}_{\text{3}}\ge \text{8,000 }\left(\text{March Constraint}\right)\hfill \\ {\text{160y}}_{\text{4}}-{\text{50x}}_{\text{4}}\ge \text{9,500 }\left(\text{April Constraint}\right)\hfill \\ {\text{160y}}_{\text{5}}-{\text{50x}}_{\text{5}}\ge \text{11,000 }\left(\text{May Constraint}\right)\hfill \\ \begin{array}{l}{\text{y}}_{\text{1}}\text{=50}\\ \text{0}{\text{.95y}}_{\text{1}}{\text{+x}}_{\text{1}}{\text{=y}}_{\text{2}}\\ \text{0}{\text{.95y}}_2{\text{+x}}_2{\text{=y}}_3\\ \text{0}{\text{.95y}}_3{\text{+x}}_3{\text{=y}}_4\\ \text{0}{}_{}\end{array}\hfill \end{array}$