Robert is the vice president of supply chain at Muchem, a manufacturer of printing inks. Given the increase in production and transportation costs in the past years, the current supply chain network is not appropriate. Robert is thinking of globalizing its supply chain given the increase in demand around the world. Robert had identified 5 countries as potential sites for new plants. Each plant can have either an annual capacity of 2 million tons with an annual fixed cost of $2.2 million or an annual capacity of $1.5 million tons with an annual fixed cost of $1.5 million. The production cost at each country is given in the local currency of the country where the plant is located. 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 the Table 1. Transportation costs from each plant to each market in U.S. dollars are shown in the Table 1. Management must come up with a plant location and transportatino plan.

Table 1- Capacity, Demand, Production, and Transportation Costs for Muchem

Transportation cost /ton	North America	Europe	Japan	South America	Asia	Production Cost / Ton
United States	$600	$1,300	$2,000	$1,200	$1,700	$10,000
Germany	$1,300	$600	$1,400	$1,400	$1,300	15000 euro
Japan	$2,000	$1,400	$300	$2,100	$900	1800000 yen
Brazil	$1,200	$1,400	$2,100	$800	$2,100	13000 real
India	$2,200	$1,300	$1,000	$2,300	$800	400000 rupees
Demand (tons/year)	1,200,000.00	900,000.00	800,000.00	1,000,000.00	600,000.00

Table2- Anticipated Exchange Rates for the Next Year

	US$	Euro	Yen	Real	Rupee
US$	1	1.993	107.7	1.78	43.55
Euro	0.502	1	54.07	0.89	21.83
Yen	0.0093	0.0185	1	0.016	0.405
Real	0.562	1.124	60.65	1	24.52
Rupee	0.023	0.046	2.47	0.041	1

First formulate a linear programming model that identifies a production/transportation plan to minimize the production and transportation costs for next year.

Then answer the following questions.

Note: Please set the interger optimality(%) to 0 in the solver options.

a. If exchange rates are expected as in table 2, Where do we locate plants and which markets should each plant supply?

b. Add the following constraint to part a and report if there is any change in the solution. Also, write the constraints in LP.

Either a small plant or a large plant can be built in a location.

c. Add the following restriction to part b and report if there is any change in the solution. Also, write the constraints in LP.

If a plant (small or large) is built in United States, then the plant in Germany must be opened.

d. Add the following constraint to part c and report if there is any change in the solution. Also, write the constraints in LP.

The number of small plants should be less than the number of large plants.

1. Attach File