PaintsMNC, a manufacturer of speciality inks, has five manufacturing plants worldwide. Their locations and capacities are shown in Table $1$ along with the cost of producing $1$ ton of ink at each facility. The production costs are in the local currency of the country where the plant is located.

Table $1$ Capacity, Demand, Production, and Transportation Costs for PaintsMNC

North America

South America

Japan

Europe

Asia

Capacity $($Tons$/$year$)$

Production $($Cost$/$Ton$)$

United States

$$1,100$

$$2,100$

$$2,300$

$$3,500$

$$3,000$

$195$

$ $18,000$

Germany

$$2,300$

$$2,500$

$$1,100$

$$2,500$

$$2,300$

$210$

$24,000$

Japan

$$3,500$

$$3,700$

$$2,500$

$$500$

$$1,600$

$175$

$19,31,000$

Brazil

$$2,100$

$$1,400$

$$2,500$

$$3,700$

$$3,700$

$250$

$53,000$ real

India

$$3,900$

$$4,100$

$$2,300$

$$1,800$

$$1,400$

$160$

$16,24,000$

Demand $($tons$/$year$)$

$160$

$240$

$110$

$110$

$260$

Table $2$ Anticipated Exchange Rates for the Next year

USD

EURO

YEN

REAL

RUPEE

USD

$1$

$0\mathrm{.}91$

$146\mathrm{.}75$

$6\mathrm{.}32$

$81\mathrm{.}22$

Euro

$1\mathrm{.}0989$

$1$

$161\mathrm{.}2637$

$6\mathrm{.}9451$

$89\mathrm{.}2528$

Yen

$0\mathrm{.}0068$

$0\mathrm{.}0062$

$1$

$0\mathrm{.}0431$

$0\mathrm{.}5535$

Real

$0\mathrm{.}1582$

$0\mathrm{.}144$

$23\mathrm{.}2199$

$1$

$12\mathrm{.}8513$

Rupee

$0\mathrm{.}0123$

$0\mathrm{.}0112$

$1\mathrm{.}8068$

$0\mathrm{.}0778$

$1$

The major markets for the inks are North America, South America, Europe, Japan, and the rest of Asia. Demand at each market is shown in Table $1.$ Transportation costs from each plant to each market in U$.$S$.$ dollars are shown too. Management must come up with a production plan for the next year.

If exchange rates are expected as in Table $2,$ and no plant can run below $50$ percent of capacity, how much should each plant produce and which markets should each plant supply?

If there are no limits on the amount produced in a plant, how much should each plant produce?

Can adding $10$ tons of capacity in any plant reduce costs?

How should PaintsMNC account for the fact that exchange rates fluctuate over time?