Chapter 3.5, Problem 7P

Explanation of Solution

Formulation of LP:

Let,

$\text{PTi}$= Part-time people starting at I PM.

$\text{Fi}$= Full-time people starting at hour I.

$\text{INVi}$= checks that have arrived before hour I and are unprocessed at time I.

$\text{Pi}$= checks processed between time I and time I + 1.

Then the a correct formulation is,

$\text{Minimize z=160}\left(\text{F10+F11+F12}\right)\text{+75}\left(\text{P2+P3}\right)$

Subject to the constraints,

$\begin{array}{l}\text{INV11 = 5000 – P10}\hfill \\ \text{INV12 = INV11 + 4000 – P11}\hfill \\ \text{INV1 = INV12 + 3000 – P12}\hfill \\ \text{INV2 = INV1 + 4000 – P1}\hfill \end{array}$

$\begin{array}{l}\text{INV3 = INV2 + 2500 – P2}\hfill \\ \text{INV4 = INV3 + 3000 – P3}\hfill \\ \text{INV5 = INV4 + 4000 – P4}\hfill \\ \text{INV6 = INV5 + 4500 – P5}\hfill \end{array}$

$\begin{array}{l}\text{INV7 = INV6 + 3500 – P6}\hfill \\ \text{INV8 = INV7 + 3000 – P7}\hfill \end{array}$

$\begin{array}{l}\text{Pi}\le \text{6500 }(\text{I = 10, }\hfill \end{array}$