A company sells five models of computers through three retail outlets. The inventories are represented by S. The wholesale and retail prices are represented by T. Compute ST and interpret the result.
S= 4 4 3 4 2
0 0 4 4 4
0 4 3 3 0
t = wholesale retail
$840 $1100
$1200 $1350
$1450 $1650
$2650 $3000
$3050 $3200
wholesale:
$840
$1200
$1450
$2650
$3050
retail:
$1100
$1350
$1650
$3000
$3200
Since S is 5x3 and T is 5x2, ST is undefined.
But, U = STT is a matrix whose (i,j) element is the total revenue for model i , wholesale or retail (j=1 or 2)
never mind. S is 3x5, so ST is defined.
To compute ST, we need to multiply the inventories (S) by their corresponding prices (T). Since there are 5 computer models and 3 retail outlets, the resulting matrix will be a 5x3 matrix.
Let's perform the calculation step by step:
ST = S * T
For the first row, we have:
ST(1,1) = S(1,1) * T(1,1) = 4 * $840 = $3360
ST(1,2) = S(1,2) * T(1,2) = 4 * $1100 = $4400
ST(1,3) = S(1,3) * T(1,3) = 3 * $1200 = $3600
For the second row, we have:
ST(2,1) = S(2,1) * T(2,1) = 0 * $1200 = $0
ST(2,2) = S(2,2) * T(2,2) = 0 * $1350 = $0
ST(2,3) = S(2,3) * T(2,3) = 4 * $1450 = $5800
For the third row, we have:
ST(3,1) = S(3,1) * T(3,1) = 0 * $1450 = $0
ST(3,2) = S(3,2) * T(3,2) = 4 * $1650 = $6600
ST(3,3) = S(3,3) * T(3,3) = 3 * $2650 = $7950
For the fourth row, we have:
ST(4,1) = S(4,1) * T(4,1) = 4 * $2650 = $10600
ST(4,2) = S(4,2) * T(4,2) = 2 * $3000 = $6000
ST(4,3) = S(4,3) * T(4,3) = 4 * $3050 = $12200
For the fifth row, we have:
ST(5,1) = S(5,1) * T(5,1) = 0 * $3050 = $0
ST(5,2) = S(5,2) * T(5,2) = 4 * $3200 = $12800
The resulting ST matrix is:
$3360 $4400 $3600
$0 $0 $5800
$0 $6600 $7950
$10600 $6000 $12200
$0 $12800 $0
Interpreting the result:
The ST matrix represents the total value of the inventories for each computer model at each retail outlet. The numbers in the matrix correspond to the wholesale and retail prices multiplied by the number of inventories. Therefore, the values in the ST matrix represent the monetary value of the inventory for each specific model and retail outlet.