a) Formulate a mathematical model that minimize the total cost while satisfy the demand forthe customers.

b)If you know that each plant can't operate under 50% of its capacity, what constraint shouldbe added to your model?

c)By adding the constraint in (b) and by using Excel find the optimal solution and identifyhow much should each plant produce, and which markets should each plant to supply.

2] Suncheml a manufacturer of printing inks, has ve manufacturing plants worldwide. Their locations and capacities are shown in the following table along with the cost of producing 1 ton of ink at each facility. 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. Transportation (the cost is per ton) and production costs from each plant to each market in US. dollars are shown in the table. Management must come up with a production plan for the next year. North South Capacity Production America Europe Japan America Asia Tons/Year CostlTon United States $600 $1,300 $2,000 $1,200 $1,700 185 $10,000 Germany $1.300 $600 $1.400 $1.400 $1.300 475 15,000 Japan $2,000 $1,400 $300 $2,100 $900 50 1,800,000 Brazil $1.200 $1.400 $2,100 $800 $2.100 200 13.000 - India $2,200 $1,300 $1,000 $2,300 $800 80 400,000 _ Demand 270 200 120 190 100 (tons/year) a) Formulate a mathematical model that minimize the total cost while satisfy the demand for the customers. b) If you know that each plant can't operate under 50% of its capacity, what constraint should be added to your model? o) By adding the constraint in (b) and by using Excel nd the optimal solution and identify how much should each plant produce, and which markets should each plant to supply