SOLUTION: 'n Beleggingsfirma bied drie aandele-opsies: Standard (x), Deluxe (y) en Gold (z) met 'n aandeleverspreiding soos in die tabel aangedui. / An investment firm offers three stock o

Question 1201037: 'n Beleggingsfirma bied drie aandele-opsies: Standard (x), Deluxe (y) en Gold (z) met 'n
aandeleverspreiding soos in die tabel aangedui. / An investment firm offers three stock
options: Standard (x), Deluxe (y) and Gold (z), with a stocks profile as indicated in the table.
10 30 40
15 10 30
10 20 30
Harmony
Billiton
Ashanti
H
B
A
x y z
Gestel die koste per aandeel vir Ashanti is R100, vir Billiton R150 en vir Harmony R175. Verder
is die inkomste per aandeel uit Ashanti R200, uit Billiton R250 en uit Harmony R270. 'n Kliënt
versoek 200 eenhede van Standard, 300 eenhede van Deluxe en 150 eenhede van Gold vir
'n persoonlike portefeulje. Stel 'n aandeleverspreidingmatriks A, kostematriks C,
inkomstematriks R en 'n eenhedematriks N saam. Pas matriksalgebra toe op hierdie matrikse
en bepaal die wins wat uit die portefeulje gemaak word. / Assume the cost per share for
Ashanti is R100, for Billiton R150 and for Harmony R175. The income per share from Ashanti
is R200, from Billiton R250 and from Harmony R270. A client requests 200 units of Standard,
300 units of Deluxe and 150 units of Gold for a personal portfolio. Compose a stocks profile
matrix A, a cost matrix C, an income matrix R and a unit matrix N. Apply matrix algebra to
these matrices and determine the profit made from the portfolio.
Answer by GingerAle(43) (Show Source): You can put this solution on YOUR website!
## Understanding the Problem
We're asked to create matrices representing a stock portfolio, its costs, income, and the number of units purchased. Then, we'll use matrix multiplication to calculate the total profit.
## Defining the Matrices
### Stock Profile Matrix (A)
* Each row represents a stock (Harmony, Billiton, Ashanti)
* Each column represents an option (Standard, Deluxe, Gold)
* The elements represent the percentage of each stock in each option.
```
A = | 10 30 40 |
| 15 10 30 |
| 10 20 30 |
```
### Cost Matrix (C)
* A row matrix representing the cost per share of each stock.
```
C = | 100 150 175 |
```
### Income Matrix (R)
* A row matrix representing the income per share of each stock.
```
R = | 200 250 270 |
```
### Units Matrix (N)
* A column matrix representing the number of units purchased for each option.
```
N = | 200 |
| 300 |
| 150 |
```
## Calculating the Total Cost and Income
### Calculating the Total Number of Shares for Each Stock
First, we need to calculate the total number of shares of each stock purchased. This can be done by multiplying the stock profile matrix (A) by the units matrix (N):
```
Total Shares = A * N
```
### Calculating the Total Cost
To find the total cost, we multiply the total number of shares by the cost per share:
```
Total Cost = (A * N) * C^T
```
* Note that we transpose the cost matrix (C^T) to ensure correct dimensions for multiplication.
### Calculating the Total Income
Similarly, to find the total income, we multiply the total number of shares by the income per share:
```
Total Income = (A * N) * R^T
```
### Calculating the Profit
The total profit is simply the total income minus the total cost:
```
Profit = Total Income - Total Cost
```
## Performing the Calculations
Using a matrix calculator or programming language, we can perform these calculations.
**Note:** The exact values for total cost, total income, and profit will depend on the specific values in the matrices.
**Interpretation:**
* The resulting profit will tell us the overall financial gain or loss from the client's portfolio.
* By analyzing the individual components (total cost for each stock, total income from each stock), we can gain insights into the performance of different investment options.
**Additional Considerations:**
* **Dividends and Capital Gains:** For a more accurate analysis, you might want to consider dividends and capital gains, which can affect the overall return on investment.
* **Risk:** The risk associated with each stock and the overall portfolio should also be considered.
* **Market Fluctuations:** Stock prices and incomes can fluctuate over time, so the calculated profit is a snapshot at a specific point in time.
By using matrix algebra, we can efficiently analyze large datasets and make informed investment decisions.

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