A&C Distributors Is a Company That Represents Many Outdoor Products

question 29

Essay

A&C Distributors is a company that represents many outdoor products companies and schedules deliveries to discount stores,garden centers,and hardware stores.Currently,scheduling needs to be done for two lawn sprinklers,the Water Wave and Spring Shower models.Requirements for shipment to a warehouse for a national chain of garden centers are shown below.

Let S_ij be the number of units of sprinkler i shipped in month j,where i = 1 or 2,and j = 1,2,or 3.Let W_ij be the number of sprinklers that are at the warehouse at the end of a month,in excess of the minimum requirement.
a Write the portion of the objective function that minimizes shipping costs.
b.An inventory cost is assessed against this ending inventory.Give the portion of the objective function that represents inventory cost.
c.There will be three constraints that guarantee,for each month,that the total number of sprinklers shipped will not exceed the shipping capacity.Write these three constraints.
d.There are six constraints that work with inventory and the number of units shipped,making sure that enough sprinklers are shipped to meet the minimum requirements.Write these six constraints.

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Definitions:

Control Group

In an experiment, a group of subjects that does not receive the treatment being tested and is used as a benchmark to measure how the other tested subjects do.

Dependent Variable

In scientific research, the variable that is tested and measured; it is 'dependent' on the independent variable.

Fat Layer

A layer in the body composed primarily of adipose tissue, which stores energy and insulates and cushions the body.

Polar Bear's Skin

The black skin of a polar bear, hidden beneath its transparent, hollow fur, which helps in absorbing sunlight to keep the bear warm in cold environments.