Question

A pension fund manager is considering investing in two shares A and B. It is estimated that,
(1) Share A will earn a dividend of 12 percent per annum and share B will cam 4 percent dividend per annum.
(2) growths in the market value in one year of share A respectively are 10 paise per Rs. 1 invested and 20 paise per Rs.1 invested in B.
He requires to invest the maximum total sum which will give,
(1) dividend income of at least Rs.600 per annum; and
(2) growth in one year of at least Rs.1000 on the initial investment.
Formulate this problem as an LP model to compute the minimum sum to be invested to meet the manager's objective.

Answer 1

Answer:

Minimum sum to be invetsed = 7000

4000 in A  & 3000 in B

Step-by-step explanation:

Sum invested = 100A  + 100B  

Dividend = 12A  + 4B ≥ 600

=> 3A + B ≥ 150

Growth = 10A  + 20B

10A  + 20B ≥ 1000

=> A + 2B ≥ 100

A          B               Dividend            Growth            Investment

50        25             700                    1000                7500

44        28              640                    1000               7200

42        29              620                   1000               7100

40        30              600                     1000              7000

38        36              600                    1100                7400  

36        42              600                     1200              7800

0          150            600                    3000               15000                

Minimum sum to be invetsed = 7000

4000 in A  & 3000 in B