Need help with this, please show work on how to use matrix multiplication step b

Question

Need help with this, please show work on how to use matrix multiplication step by step. Please dont just give answers, please show work

Four departments of a company need to order the following amounts of the same(a) Use matrix multiplication to get a matrix showing the comparative costs for roducts each department for the products from the two suppliers Memo Pads Department Paper Tape Binders Pens A B Dept. 17 88 Dept. 2 53 71 Dept. 335 47 Dept. 44442 The unit price (in dollars) of each product is given below for two suppliers Supplier A Supplier B (b) Find the total cost over all departments to buy products from each supplier. From which supplier should the company make the purchase? Ta Binders Memo Pads Pens XA. The total cost for supplier A is S and the total cost for supplier B is 4 S so the company should make the purchase from supplier B B. The total cost for supplier A is $ 203 and the total cost for supplier B is S 248, so the company should make the purchase from supplier A.

Explanation / Answer

We have 2 matrices here

First Matrix has 4 rows (Depart.1, Dept.2 , Dept 3, Dept 4) & 5 columns namely Paper,Tape,Binders etc.

Second Matrix which has 5 rows and 2 columns Rows are namely (Paper, Tape. Binders etc.)

According to MAtrix Rule when we mupltiply two matrices of different form that is lets assume 1a matrix of form (m rows and n columns) and 1b matrix of form (n*k) then 1acan be multiplied with 1b because the multiplicity of two matrices is possible when number of columns of one matrix should be equal to number of rows of other matrix(1a*1b=m*n*n*k=m*k new matrix of different form

In our case to find cost of store A & B we will multiply 1st matrix with 2nd matrix not the other way round,

Our 1st Matrix has struvture of 4*5 and 2nd Matrix has a structure of 5*2 therfore resultant matrix is (4*5*5*2)=4*2(4 rows and 2 columns)

When we multiply 1 eow with 1 column of matrix at a time

1st component a11 =9*3+5^1+4*5+3*4+7^1=71, a22=(5*9+5*1+4*3+3^4+7*2=88

Similary for other aij cab be compuyed

aij = ith row and j th column component in resultant role of size 4*2

In Part B just sum of column in resultant 3 matrix will give you total cost of A & B then comparing we getTC a=$203 ^ TC b=248

Optoin B is correct

Department Paper Tape Binders Memo Pads Pens 1 9 5 4 3 7 2 7 2 2 3 8 3 4 5 2 0 8 4 0 2 4 4 6

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