Question

A hard ware company has 60 different retail stores in which 1500 different products are sold. Write a paragraph or tow explaining why matrices provide anefficient method on inventory control, and what matrix operations would be of use

Answer 1

Refer to question brainly.in 35825.  You have a lot of information.

You can use matrix subtraction to prepare the Order.  The matrix addition is used for updating stock with the supplies. Transpose is used for column and row matrices. You can use matrix multiplication to get total cost, total profit for one retail stores or all retail stores together.  

Matrices provide efficient method because large number of products and large number of shops can be handled in a compact manner. Manual methods for individual products will be difficult and error prone. It is efficient because same operation is done for all elements in one row. Optimized methods and programs are available. It is easy to identify quantities according to row or column.

Let A be the matrix of current stock. This is maintained by 
Let B be the matrix of supplies. 

Products is a 1 x 1500 matrix.  Let Np = 1500
$Products = \left[\begin{array}{ccccccc}Shampoo&brush&paste&horlicks&rice&cereals&.. \\\end{array}\right]$

RetailStoresList is a 60 * 1 matrix. Let Ns = 60.

$RetailStoresList= \left[\begin{array}{c}Hyderabad&secunderabad&market\\JBS&ringRoad&Uppal\\SD Road&Ameerpet&Nampalli&..&..\end{array}\right]$

Stock is a 1 * Np matrix at one stores.

$OneStoreStock = \left[\begin{array}{cccccc}s1&s2&s3&s4&s5&..\end{array}\right]$

Stock at all Stores is a Ns * Np matrix: Each row represents stock at one RetailStores. 

AllStoresStock = $\left[\begin{array}{cccccc}s1,1&s1,2&s1,3&s1,4&s1,5&..\\s2,1&s2,2&s2,3&s2,4&s2,5&..\\:&:&:&:&:&:\\s60,1&s60,2&s60,3&s60,4&s60,5&..\end{array}\right]$

As the products are sold at one stores, the OneStoreStock is updated. You can have a matrix with threshold values for each product. If quantity goes below this value, then that product is ordered from the head office. This matrix could be same for all retail stores.

ThresholdStock =$\left[\begin{array}{cccccc}t1&t2&t3&t4&t5&..\end{array}\right]$

OrderStock is again of the same size. 
OrderStock =$\left[\begin{array}{cccccc}O1&O2&O3&O4&O5&..\end{array}\right]$

Now the head office combines all these orders and could prepare combined matrix. This is 60 * 1500 size.

TotalOrder=$\left[\begin{array}{cccccc}O1,1&O1,2&O1,3&O1,4&O1,5&..\\:&:&:&:&:&:\\O60,1&O60,2&O60,3&O60,4&O60,5&..\end{array}\right]$

If the prices of the products is maintained as Np * 1 = 1500 * 1 matrix then

Prices = $\left[\begin{array}{c}ShampooPrice&BrushPrice&pastePrice&HorlicksPrice&:\end{array}\right]$

TotalCost = TotalOder x Prices 
       The TotalCost matrix is a Ns * 1 matrix with each entry for one stores at one locality.

When supplies arrive, the supply matrix could be 

TotalSupply=$\left[\begin{array}{cccccc}O1,1&S1,2&S1,3&S1,4&S1,5&..\\:&:&:&:&:&:\\S60,1&S60,2&S60,3&S60,4&S60,5&..\end{array}\right]$

AllStoresStock = AlStoresStock + TotalSupply 

That updates all the stock.

 For each stores one matrix (1*Np size) and there is one matrix for all stores (Ns * Np size)

      LeastSoldGoods = OneStoreStock on Sunday Night - OneStoreStock on Friday Evening

This matrix gives the least sold items. So the stores can relevant action to put them on SALES promotional offers.