International City Trust ICT invests in shortterm corporate

International City Trust (ICT) invests in short-term corporate bonds and construction loans. To encourage a diversified portfolio, the Board of Directors has placed limits on the amount which can be invested in any one type of investment. ICT has $500,000 to invest. The Board has recommended that at least 20 percent but no more than 30 percent should be invested in construction loans and that investment in short-term corporate bonds be twice as much as construction loans. The returns on the investment arc 11 percent for corporate bonds and 15 percent for construction loans. Formulate as a linear programming problem.

Solution

Let X1 denote in the short-term corporate Bonds and X2 denote Construction loans

Object function Max Z = 0.11X1 + 0.15X2

Subject of constraints

         x1 + x1 < 500,000 (total investment)

                  x2 >= 100,000 ( Atleast 20% of investment on Corporate loans)

                   x2 <= 150,000 (Atmost 30% of investment on Corporate loans)

                   x1 = 2 x2    (corporate bond be twice as much as construction loans)

Non negative constraints, x1 , x2 >= 0