A financier plans to invest up to $300,000 in two projects. Project A yields a r

Question

A financier plans to invest up to $300,000 in two projects. Project A yields a return of 10% on the investment, whereas Project B yields a return of 15% on the investment. 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?

What is the maximum return?
$

Explanation / Answer

Let investment in project A be = X
Let investment in project B = Y;
Return on A = 10% of X = 0.1 X
Return on B = 15% on Y = 0.15 Y
We know that total budget = 300,000$
X+Y <= 300,000$
Returns= 0.1X + 0.15Y => We are to maximise this function of returns;
Investment in project B is riskier so maximum of only 40% can be invested into it, so
Y <= 0.4 (X+Y) ;
Here since both investments yield positive returns and cost of capital is not given, we will decide that we are going to invest the entire amount;
So X+Y = 300,000$
Y<= 0.4(300,000) = 120,000$

Thus, we are to maximise 0.1X + 0.15 Y
Subject to constraints :
X+Y = 300,000
Y<= 120,000
Since Y has higher returns, we will try to maximise Y and use up the entire limit of 120,000 restriction;
So Y = 120,000
That leaves X = 300,000 - 120,000 = 180,000$

So for maximum returns:
So investment in project A = 180,000$
Investment in project B = 120,000$
And maximum returns is = 180,000* 0.1 + 120,000*0.15 = 18,000 + 18,000 = 36,000$

So maximum return is 36,000$ on a capital of 300,000$ or = 12% returns;

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