Question

Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to $600,000 in two projects. Project A yields a return of 10% on the investment of x dollars, whereas Project B yields a return of 14% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 45% of the total investment. How much should she invest in each project to maximize the return on her investment P in dollars? Maximize P = subject to the constraints amount available for investment allocation of funds x ≥ 0 y ≥ 0

Answer 1

Given

A financier plan to invest up to $600,000 in two projects A and B

Project A yields return of 10% on the investment of x dollars = 0.1x

Project B yields return of 14% on the investment of y dollars = 0.14y

x+y <= 600,000

So

Maximize P = 0.1x + 0.14y

Investment in project B should not exceed 45% of the total investment = 0.45 * 600000 = $270,000

y<= 270,000

Now Investment in project A = 600000-270000 = $330,000

Maximize P = 0.1 (330000) + 0.14(270000) = $70800

So

Profit = $70800

x>=0

y>=0