IE $3553$ Deterministic Operations Research$-$Homework $2$

i$)$ A canning company operates two canning plants. There are three growers willing to supply fresh fruits in the following amounts:

Amy: $200$ tons at $\backslash (\backslash$$ $10/\backslash )$ ton

Bill: $300$ tons at $\backslash (\backslash$$ $9\backslash )$ hton

Cody: $400$ tons at $\backslash (\backslash$$ $8/\backslash )$ ton

Shipping costs in dollars per ton are:

Plant capacities and Jabour costs are:

The carned fruits are sold at $\backslash (\backslash$$ $40/\backslash )$ ton to the distributors. The company can sell at this price all they produce. How should the company plan its operations at the two plants to maximige its profits?

a$.$ Formulate the problem as a linear programming model. Clearly define your parameters, decision variables and explain your constraints.

b$.$ Write a CPLEX code for your problem and interpret the results. What do you think would happen if you were to change some parameters? Give specific examples.

Formulate your mathematical model in the close form as much as possible.

Write your mathematical model in a word document with Equation $($Denklem$).$

How to find the Equation tool: Insert $\backslash (\backslash$rightarrow $\backslash )$ Equation $($Ekle $\backslash (\backslash$rightarrow $\backslash )$ Denklem$)$