Question

A consonsultant wishes to invest up to a total of $25000 in two types of securities, one that yields 10% per year and another than yields 8% per year. They believe that the amount invested in the first security should be at most one third of the amount invested in the second security. What investment program should the consultant pursue in order to maximize income? (Use constraint inqualities with objective function)

Answer 1

Let, the amount invested in first security is x and in second security is y

Total investment in two types of security is $25000 implies

Amount invested in first security is atmost 1/3 the amount in the second security implies

Also,

The objective function is the amount of yield per year which is

Plot the inequalities and find the feasible region

The maximum of the income occurs at the corner points of the feasible region. Find the function value at A(0,25000) and B(25000/4, 75000/4)

Therefore, the yield is maximized for the following investment program