Answer to Question #271595 in Operations Research for alyss

Question

A retired employee wants to invest no more than ₱1,500,000 by buying a stock from a well-known bank and of a university. The stock from the bank offers 7% interest while the stock of a university pays a 5% return. He decided to invest no more than ₱800,000 in the stock from the bank and at least ₱300,000 in the stock of the university. Also, he wants his investment in the stock from the bank to be smaller than his investment in the stock of the university. How much stock should he buy for each investment to maximize his profit? Given that x and y are non-negative, what are some of the constraints? Check whether each constraint is the correct expression for the problem. *

Answer 1

$\displaystyle z= \frac{7}{100}x +\frac{5}{100}y\\ \text{Subject to} \\ x+y \leq 1500000\\ x \leq 800000\\ y \geq 300000\\ x < y, x\geq 0, y\geq0\\ \text{Now change the inequalities to equalities and plot on the graph}\\ \text{As we see in the the attached graph, the corner points are given by}\\ (300000,300000), (750000, 750000 ), (800,000,700000)\\ \text{substituting the points above in our objective function,we have that}\\ \text{(800,000,700000) is the maximum point. Hence, the investor should invest 800000}\\ \text{into the bank and 700000 into the university.}$