The sale of an IIT unit produces an income of $21 and that of an IIS $30. The demand must be satisfied the same day it is presented (it does not matter if the demand is completed until the end of the day), otherwise it will be lost. The production of a certain day can be used to satisfy the demand of that same day or that of the rest of the week; that is, glasses produced on Monday can be used to satisfy demand on Monday, Tuesday, or Wednesday, and glasses produced on Tuesday can be used to satisfy demand on Tuesday or Wednesday. Importantly, because the rest of the week the plant produces other models, models IIT and IIS cannot be left in stock, meaning there is never any stock in inventory on Monday morning. Because of increased handling costs, it costs $4.25 to hold an IIT unit and $5.30 to hold an IIS in inventory from one day to the next. One unit of lost demand results in a total penalty cost of $2 for one unit of IIT on Monday, $4 on Tuesday, and $5 on Wednesday. The unit penalty costs for an IIS unit are $5 on Monday, $10 on Tuesday, and $11 on Wednesday. Demand varies greatly, so management is considering two generic demand patterns, high before summer and low after summer, as shown in the following tables.

On your first day on the job, the plant owner tells you that he thinks the IIT units contribute $42 per labor hour, while the IIS contributes $40 per labor hour, and that he thinks the company should first satisfy all IIT demand, starting Wednesday, then Tuesday and then Monday, finally using the remaining capacity (if any) to produce IIS units, however, all these comments are only assumptions that the owner considers but are not necessarily correct.

Finally, the owner has asked you to plan the allocation of craftsmen for the production of the IIT and IIS models so that the company can achieve the highest possible total profit.

1. What are the sets (indices) in this problem? 2. What are the parameters? 3. What are the decision variables? What type of variable is each?

1. Program in GAMS (LINGO) the mathematical model that you developed in step 1, so that in the program you can only modify the demand to obtain the results of the high season and the low season. You can make the changes you think are necessary in the model proposed in stage 1.

2. Using the GAMS program (LINGO), obtain the optimal solution and record the obtained values of the objective function and the decision variables.

3. Interpret these results to generate a final report that the owner can understand (consider that he knows nothing about linear programming). It is recommended to use graphs and/or tables to represent these results.

\begin{tabular}{|l|l|l|l|} \hline \multicolumn{4}{|l|}{ Temporada baja despus de verano } \\ \hline & Lunes & Martes & Mircoles \\ \hline IIT & 240 & 48 & 64 \\ \hline IIS & 160 & 32 & 64 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{4}{|l|}{ Temporada baja despus de verano } \\ \hline & Lunes & Martes & Mircoles \\ \hline IIT & 240 & 48 & 64 \\ \hline IIS & 160 & 32 & 64 \\ \hline \end{tabular}