In your own words, describe the special cases of integer programming and binary programming: what makes these problems different? Give an example of each, pointing out why they must be an integer or binary programming problem as opposed to a standard linear programming problem.
In your own words, explain what a “shadow price” is. Give an example of a shadow price and what it would mean if the associated constraint was changed.
The AppleBerry Company has three warehouses where it stores its tablet computer devices and four distributors that place these products in retail stores and online. Each warehouse holds 5000 devices. Because of the various distances between the warehouses and the distribution centers, there are different costs to ship the devices from each warehouse to each distributor. The cost per device for shipping between the warehouses and distributors is given in the table below. Additionally, each distributor has calculated an estimated monthly demand for the tablet and does not want to receive any more tablets than this estimated demand.
Furrel’s Ice Cream Company ships ice cream in bulk from its manufacturing facility to its 25 retail outlets. Furrel’s has categorized its retail outlets into four types, each of which sells a certain level of ice cream per week, measured in pounds. Furrel’s ships its ice cream in two different size reusable containers: a 6-pound container and a 10-pound container. The company currently has 200 6-pound containers and 25 10-pound containers. The company would like to minimize the amount of excess ice cream shipped to each store while making use of its existing reusable containers. For example, store type 1 needs 25 pounds of ice cream a week. Furrel’s could ship this in one 10-pound container and three 6-pound containers for a total of 28 pounds (3 pounds excess) or in two 10-pound containers and one 6-pound containers (1 pound excess). However, with only 25 10-pound containers available, it is not clear that this is the best choice for this type of store.