$***$ This is the most Important part $***$ Make sure to identify and define the decision variables, and formulate the objective function and constraints for each problem. $(Ill$ put these $in$ excel $to$ find quality answers$)(simple$ terms are easiest $to$ understand$)$

$1.$ Sunchem, a manufacturer of printing 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 major markets for the inks are North America, Europe, Japan, South America, 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 in Table $1.$ Management must come up with a production plan for the next year.

a$.$ If no plant can run below $50$ percent capacity, how much should each plant produce and which

markets should each plant supply?

b$.$ If there are no limits on the minimum amount produced in a plant, how much should each plant

produce?

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