Cookout Inc. manufacturers charcoal grills popular among college tailgating fans. Cookout Inc. has been asked by SCU to manufacture and delivery their O-Matic grill over the next five hockey weekends. Required contract deliveries over this five-week horizon are: 80, 230, 170, 150, and 200 units. Production costs per grill vary over time, due to the availability of Cookout Inc. workforce. The estimated production cost per grill over the next five weeks is $48, $46, $52, $42, and $50, respectively. To take advantage of the fluctuation in production costs, Cookout may choose to produce more grills for delivery in later weeks. However, this decision is accompanied by storage costs of $10 per grill per week. Also, because of marketing commitments, at least 25% of the grills must be made in the first two weeks.

1. Formulate a linear program to determine the lowest cost production schedule. Please clearly define all terms in your model and distinguish between your input parameters and decision variables. (Note, you are not required to solve the model, just formulate it).

2. How would your model change if the weekly holding cost of $10 per grill doubled every week? Please comment on how this influences the objective function, the constraints, and the decision variables.

(All data is given in paragraph above)