LP Formulation paragraphs

3) Method of Solving the problem (Developing an LP, Calculating the identified constraints such as freezer space, filleting capabilities, etc)

For the Salmones Puyuhuapi Case Study the objective is to maximize profits. The five product

types to be considered are frozen enteros, fresh enteros, frozen fillets, fresh fillets, and frozen portions.

Our objective value is defined as the profits from each live weight bin minus the cost of producing each

bin. Broken down further, it is important to note that each weighted bin has its own cost (in terms of

finished kilograms) and its own selling price. Freezer Space is calculated by the live weight of each bin

multiplied by the sum of each type of product where the yield percentage is taken into account. This is

only important for frozen products and has a capacity of 120,000 pounds per day which was calculated

in Section II. Trimming Capabilities are defined as twice the number of fish that are either fresh fillets,

frozen fillets, or portions and has a capacity of 67,200 fish per day. Enteros are whole fish thus they are

not a burden on the trimming constraint. Filleting Capabilities are defined as the fish that have already

been trimmed and need to be filleted with a capacity of 28,800 fish per day. Similar to the trimming

capabilities, the whole fish are not a burden on the filleting capabilities. Portioning Capabilities are

defined as the number of fish allocated for portioning. As mentioned in Section II, the smaller fillets are

sent to the portioning machine.

In order to obtain the best possible solution, we decided to formulate a Linear Programme

based on the aforementioned calculations to maximize the profits with respect to the constraints

outlined in Section II. We used Microsoft Excel and its Solver capabilities to obtain our optimal solution.

We decided to use Linear Programming over Integer programming because while we are not capable of

producing fractional amounts of product we are also dealing with average weights per bin thus making

an integer solution significantly less valuable.