A car manufacturer has production plants in Germany, the United Kingdom, and France

and exports to some other countries. The manufacturer$$s supply chain includes the

manufacturer, distributors and retailers. The plant in Germany wants to export $5000$ cars,

the UK plant, $2500$ cars, and the France plant, $3000$ cars. Cars are not shipped directly

from plants to retailers; they are first shipped to distributors in Egypt and the UAE, who in

turn export cars to retailers$$ countries. Distributors do not stock cars; they export

whatever they receive from manufacturers. The demand for cars from India is at least

$2000$ cars, South Africa, $4000$ cars; and Singapore, $1000$ cars. Since the customs rules

and currency rates are different in these countries, the transportation costs in dollars to

ship a car from production plants to distributors are:

Country Egypt $(4)$ UAE $(5)$

Germany $(1)300400$

UK $(2)350450$

France $(3)250300$

The costs of transshipping a car in dollars from Egypt and the UAE to the three other

countries are shown in the following table:

Country India $(6)$ South Africa $(7)$ Singapore $(8)$

Egypt $(4)450500600$

UAE $(5)400350550$

The manufacturer wants to determine the export mix of cars that will minimize

transportation costs.

a$)$ Formulate a linear programming model for this problem.

b$)$ Solve using Excel Solver.