Answer to Question #245219 in Operations Research for joy11

Question

A trust fund is planning to invest up to PhP6000 in two types of bonds: A and B. Bond A is safer than bond B and carries a dividend of 8 percent, and bond B carries a dividend of 10 percent. Suppose that the fund's rules state that no more than PhP4000 may be invested in bond B, while at least PhP1500 must be invested in bond A. How much should be invested in each type of bond to maximize the fund's return?

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Answer 1

x = amount invested in Bond A

y = amount invested in Bond B

Linear optimization function is:

Maximize z = 0.08x + 0.1y

subject to:

x + y ≤ 6000

x ≥ 1500

y ≤ 4000

y ≤ 1/2 x

Point z = 0.08x + 0.1y

A (1500, 0) = (0.08*1500) + (0.1*0) = 120

B (1500, 750) = (0.08*1500) + (0.1*750) = 195

C (4000, 2000) = (0.08*4000) + (0.1*2000) = 520

D (6000, 0) 480 = (0.08*6000) + (0.1*0) = 480

As shown above, the fund's return would be highest at the point of (4000, 2000). So, PhP4000 should be invested in Bond A and PhP2000 in Bond B...