Using the information and the data provided in the case and on the supplementary Excel spreadsheet that is available, develop a multi $$ period linear programming $($LP$)$ formulation to deal with an optimization problem of your choice relevant to the case. $($The scope of the chosen problem does not have to incorporate the entire set of data provided in the text and $/$ or in the Excel supplement. However, the scope should be coherent, using part, not all, of the information and data provided in the case and $/$ or in the Excel supplement.$)$ Do not solve the formulated problem.

a$)$ Provide the assumptions involved in the LP formulation.

b$)$ Define $($in mathematical notation and in words$)$ the decision variables.

c$)$ Define $($in mathematical notation and in words$)$ the parameters involved in the objective function and the constraints.

d$)$ Write the LP formulation in its entirety using the relevant parameter values provided in the case. $($i$.$e$.,$ Do not write C$1$X$1.$ Instead, provide the value for C$1$ from the case.$)$