Question

As you begin your new job as an engineer, your boss assigns your first task of optimizing the manufacturing warehouse. Your company houses a variety of different products in the warehouse. Each product is placed on a dedicated shelf in the warehouse. Assume that all of the same type fit on a single warehouse shelf, and that for simplicity, a shelf can hold only a single type of item. The warehouse has two types of shelving:

1. Shelving in prime locations, reserved for the most popular products so they can be quickly accessed.
2. Shelving in a less convenient area of the warehouse, which take longer to access. The products not assigned to the prime locations are stored here.

Use this information to answer the following questions.

-You would like to determine how many different ways you can recommend that the products be stored within the prime and the less convenient shelving positions. What would you need to calculate?

a.Permutation, without replacement

b.Permutation, with replacement

c.Combination

-Calculate how many different ways you can recommend that the products be stored if the company has 12 total products and only 4 shelves that are in prime locations.

-Assume that a subset of the products is selected to be placed on shelves in prime locations. Further assume that each of the prime storage locations is labeled with a unique identification number (e.g., if there were four shelves in prime locations, the shelves would be labeled 1, 2, 3 or 4). You would like to determine how many possible ways are there in which products assigned to prime storage locations. What would you need to calculate?

a.Permutation, with replacement

b.Combination

c.Permutation, without replacement

-Calculate how many different ways you can recommend that the products be stored if the company has 12 total products and only 4 shelves that are in prime locations.

-Assume that a subset of the products is selected to be placed on shelves in prime locations. Further assume that each of the prime storage locations is labeled with a unique identification number (e.g., if there were four shelves in prime locations, the shelves would be labeled 1, 2, 3 or 4). You would like to determine how many possible ways are there in which products assigned to prime storage locations. What would you need to calculate?

a.Permutation, with replacement

b.Combination

c.Permutation, without replacement

-Your company has a total of 12 products; 4 of the 12 products are selected to be placed in the prime storage locations of the warehouse. Each of the prime storage locations is labeled with a unique identification number as explained above. Calculate how many possible ways are there in which products assigned to prime storage locations.

Answer 1

As per the guidelines I am suggested to answer only first four subparts at a time, please ask rest of the sub - parts separately. I will be happy to help.

a) Answer - C) Combination will be used, as we have to only decide which products to send to primary area and which products to send to secondary area depending upon the number of shelves in the primary area.

b) Different ways you can recommend that the products be stored if the company has 12 total products and only 4 shelves that are in prime locations:

= 12C4 = 495 Answer

c) Here we will use C) Permutation without replacement, as the shelves are labelled now.

d) Different ways you can recommend that the products be stored if the company has 12 total products and only 4 shelves that are in prime locations which are labelled 1,2,3 and 4:

= 12C4(4!) = 495 * 24 = 11,880 Answer

Please upvote if this helps. Thanks.