Mathematical Modeling
Mathematical Modeling
Espresso Royale buys coffee beans from n roasting plants for each of their m coffee shops. Each coffee shop needs pj pounds of coffee beans, where 1 ≤ j ≤ m. Espresso Royale can purchase as much as bi pounds of coffee beans from roasting plant i, where 1 ≤ i ≤ n. It costs ci dollars to purchase a pound of coffee beans from roasting plant i. In addition, there is a transportation cost of hij dollars to deliver coffee beans from roasting plant i to coffee shop j, regardless of how many pounds of coffee beans are being transported.
(a) Formulate a generic linear programming model to determine how many pounds of coffee beans to transport from each roasting plant to each coffee shop to minimize the total cost of purchasing and transporting coffee beans.
Espresso Royale also needs to hire the trucks and their drivers to transport the coffee beans. Each truck can only be used to transport coffee beans from a single roasting plant to a single coffee shop. There is a fixed cost of K associated with hiring each truck. A truck can transport f pounds, but it is not required to go full.
(b) How would you incorporate this information into your model?
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