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68 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

Figure 2.21 Graphical Solution of a Two-Variable Linear Programme with General
Notation

x 2
7

6

5

4 Constraint 2

3 Constraint 1
Optimal Solution
x = 2, x = 2
2
1
Optimal Value = 3 x + 2 x = 10
1
2
2
3 x + 2 x = 6
1
2
1

x 1
0 1 2 3 4 5

WORKED EXAMPLE

lair & Rosen PLC (B&R), is a UK based brokerage firm that specializes in building investment portfolios
B designed to meet the specific needs of its clients who are mostly private individuals wishing to invest their
savings in stocks and shares. One client who contacted B&R recently has a maximum of £500 000 to invest.
B&R’s investment advisor has decided to recommend a portfolio consisting of two investment funds: an
Internet fund, where the companies are all active in Internet businesses of one kind or another, and a Blue Chip
fund which is more conservative and traditional. The Internet fund has a projected annual return over the next
few years of 12 per cent, while the Blue Chip fund has a projected annual return of 9 per cent. The investment
advisor has decided that at most £350 000 of the client’s funds should be invested in the Internet fund. B&R
services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the
two investment alternatives, has a risk rating of 6 for every thousand £s invested. The Blue Chip fund has a risk
rating of 4 per thousand £s invested. So, for example, if £10 000 is invested in each of the two investment

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