Chapter 3, Problem 63RP

Explanation of Solution

Formulation of LP:

$\text{DO}$= Dollars at the end of the day

$\text{PO}$= Pounds at the end of the day

$\text{MO}$= Marks at the end of the day

$\text{YO}$= Yens at the end of the day

$\text{ij}$= Billions of units converted from $\text{i}$ to $\text{j}$

$\text{i}$, $\text{j}$ can be $\text{d,p,m,y}$

Where,

$\text{d}$ is for dollar

$\text{p}$ is for pound

$\text{m}$ is for marks

$\text{y}$ is for yen

The formulation of problem is more like, transportation problem. Here, sources at one end and demand at the other. Here, source is the amount of dollars, pounds, marks and yen and at the beginning of the day and demand is the amount want at the end of the day. With variable $\text{ij}$, convert from one currency $\text{i}$ to another currency $\text{j}$.

Requirement Constraints:

Here, it is required 6 Billion Pounds, 1 Billion pounds and 8 Billion marks.

$\begin{array}{l}\text{DO}\ge \text{6}\\ \text{PO}\ge \text{3}\\ \text{MO}\ge \text{1}\\ \text{YO}\ge \text{10}\end{array}$

Supply Constraints:

At the start of the day, there are 8 Billion dollars, 1 Billion pounds and 8 Billion marks. So,

$\begin{array}{l}\text{dd+dp+dm+dy=8}\\ \text{pd+pp+pm+py=1}\\ \text{md+mp+mm+my=8}\\ \text{yd+yp+ym+yy=0}\end{array}$

Demand constraints:

While converting from one currency to another, it need to keep account of the conversion rate