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.
Store Type
Type 1 Type 2 Type 3 Type 4.
Pounds of Ice Cream needed 25 40 50 100
Number of Stores 10 5 4 6
Given this current store configuration and the number of reusable containers available, how many 6-pound and 10-pound containers should be used to ship to each store in order to minimize the excess ice cream?
How much excess ice cream will this lead to each week?
Should Furrel's purchase more 6-pound containers or more 10-pound containers? Why?