Formulate but do not solve the following exercise as a linear programming problem.A financier plans...

Jaxon Hamilton

Jaxon Hamilton

Answered

2022-07-24

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 40% of the total investment. How much should she invest in each project to maximize the return on her investment P in dollars, and what amount is available for investment?

Answer & Explanation

abortargy

abortargy

Expert

2022-07-25Added 19 answers

Step 1
Given, 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.
Then, the total return from two investments is = $ [ ( 10 % × x ) + ( 14 % × y ) ]
= $ [ ( 0.1 × x ) + ( 0.14 × y ) ] = $ ( 0.1 x + 0.14 y )
Let the total return be $ z
Them we have,
z = 0.1 x + 0.14 y
Since financier plans to invest up to $600,000 in two projects, then we have,
x + y 600000
Here, the total investment is = $ ( x + y )
Since the investment in Project B should not exceed 40 % of the total investment, then we have,
x 40 % × ( x + y ) i.e.,   x 0.4 × ( x + y ) i.e.,   x 0.4 x + 0.4 y i.e.,   x 0.4 x 0.4 y i.e.,   0.6 x 0.4 y i.e.,   5 × 0.6 x 5 × 0.4 y i.e.,   3 x 2 y
Now the linear programming problem becomes,
max   z = 0.1 x + 0.14 y subject to   x + y 600000 3 x 2 y x 0 y 0

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