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
ST =
29210 33150
28600 31400
17100 19350
choose one of the following that best describes the above:
a) The entries represent the profits the retail outlets can get for each model of computer.
b) The entries represent the inventory quantities at the three outlets.
c) The entries represent the wholesale and retail values for each model if the outlets were combined.
d) The entries represent the wholesale and retail values of the inventories at the three outlets.
S is 3x5
T is 5x2
So, you get a 3x2 matrix, one row for each outlet, one column for wholesale/retail.
So, what do you think?
I think it's c
so, where's the entry for model 4?
To compute ST, you need to multiply the values in the S matrix (inventories) by the corresponding values in the T matrix (wholesale and retail prices). Here's how you do it:
1. Multiply each element in the S matrix by the corresponding element in the T matrix.
2. Add up the products to get the resulting matrix, which is ST.
Using the given matrices:
S =
4 4 3 4 2
0 0 4 4 4
0 4 3 3 0
T =
840 1100
1200 1350
1450 1650
2650 3000
3050 3200
To calculate ST, you multiply each element in S with its corresponding element in T and sum the results:
ST =
(4 * 840 + 4 * 1100) (4 * 1200 + 4 * 1350)
(0 * 1450 + 0 * 1650) (4 * 2650 + 4 * 3000)
(0 * 3050 + 4 * 3200) (3 * 840 + 3 * 1100)
ST =
(3360 5100)
(0 21200)
(12800 6570)
Interpretation:
The resulting matrix ST represents the wholesale and retail values for each model of computer if the three outlets were combined. Therefore, the correct answer is option c) The entries represent the wholesale and retail values for each model if the outlets were combined.