Exercise $3$ of Chapter $5$ as below. The optimization model formula and Excel file $($Not screenshot$)$ are required. In the model, specify decision variables, objective function, and constraints; also upload the Excel file. Table $5-6$ Capacity, Demand, Production, and Transportation Costs for Sunchem

Sunchem, a manufacturer of printing inks, has five manufacturing plants worldwide. Their locations and capacities are shown in Table $5-6$ 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. 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 $5-6.$ Transportation costs from each plant to each market in U$.$S$.$ dollars are shown in Table $5-6.$ Management must come up with a production plan for the next year.

a$.$ If exchange rates are expected as in Table $5-7,$ and no plant can run below $50$ percent of capacity, how much should each plant produce and which markets should each plant supply?

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

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

d$.$ How should Sunchem account for the fact that exchange rates fluctuate over time?