Homework $4$

$1.$ Suppose you are managing production of three products $($X$,$ Y$,$ Z$)$ in three different

locations $($A$,$ B$,$ C$).$ In each location facilities can run up to $8$ hours per day. The table below

provides data about productivity per hour at each location.

Production per hour Price

location A location B location C

Product X $213200$

Product Y $322180$

Product Z $231150$

Your firm is renting the production space in each location. Current rent agreements allow

for up to $250,300,$ and $250$ days of production in locations A$,$ B$,$ and C respectively.

a$)$ Construct the $$bad$$ GAMS code using a variable with no sets for each product made at

each location. Solve the model in GAMS.

b$)$ Construct a $$good$$ model in GAMS using sets notation where choice variables are two

dimensional. No numbers can be used in the $..$ equations. Solve the model and

confirm that the result is the same as in a$)$

c$)$ Report the optimal production plan for X$,$ Y$,$ and Z

d$)$ If you wanted to rent additional days of production where would you be most likely to

expand?

e$)$ What is the maximum you would be willing to pay to rent another day at each location?

Turn in your GAMS codes and only the table reports for variables and equations from the