Question

A beverage company delivers three type of drinks which are Milk(M), Carbonated drinks(C) and Juice (J) to four stores (A, B, C, D) for a period of two month.

The number of pets of each type of beverage delivered to four stores in first month is represented in Matrix K and second month is Matrix L
M C J M C J
A[8 4 3] A[1 3 1]
K=B[2 2 2] L = B[2 7 2]
C[1 3 1] C[8 3 4]
D[3 1 3] D[9 2 6]

Calculate the total number of pets delivered over the period of 2 months to each store.
Suppose, the price charged for pet of each type of drink is given by the matrix.
M[225]
C[195]
J [212]

Answer 1

The total revenue generated for each store over the two months is as follows:

A: $4962

B: $3915

C: $4452

D: $6888

To calculate the total number of pets delivered over the two months to each store, we need to find the element-wise sum of matrices K and L. The resulting matrix, T (Total), will represent the total number of pets delivered to each store.

Matrix K:

`\[ \begin{bmatrix} 8 & 4 & 3 \\ 2 & 2 & 2 \\ 1 & 3 & 1 \\ 3 & 1 & 3 \end{bmatrix} \]`

Matrix L:

`\[ \begin{bmatrix} 1 & 3 & 1 \\ 2 & 7 & 2 \\ 8 & 3 & 4 \\ 9 & 2 & 6 \end{bmatrix} \]`

Total Matrix T = K + L:

`\[ \begin{bmatrix} 9 & 7 & 4 \\ 4 & 9 & 4 \\ 9 & 6 & 5 \\ 12 & 3 & 9 \end{bmatrix} \]`

Now, we can calculate the total number of pets delivered to each store by summing the elements in each column of matrix T.

Total for Store A: 34 pets

Total for Store B: 25 pets

Total for Store C: 24 pets

Total for Store D: 24 pets

The price charged for each type of drink is given by the matrix:

`\[ \begin{bmatrix} 225 \\ 195 \\ 212 \end{bmatrix} \]`

To find the total revenue generated for each store, we can multiply the transpose of the price matrix by the corresponding column vector from matrix T.

Revenue for Store A:
`\(225 * 9 + 195 * 7 + 212 * 4 = 4962\)`

Revenue for Store B:
`\(225 * 4 + 195 * 9 + 212 * 4 = 3915\)`

Revenue for Store C:
`\(225 * 9 + 195 * 6 + 212 * 5 = 4452\)`

Revenue for Store D:
`\(225 * 12 + 195 * 3 + 212 * 9 = 6888\)`