Finance-investments Natsona has at most $50,000 to invest in the common stocks o

Question

Finance-investments Natsona has at most $50,000 to invest in the common stocks of two companies. he estimates that an investment in company A will yeild a return of 10%, whereas an investment in company B, which he feels is a riskier investment, will yeild a return of 20%. If he decides that his investment in the stock of company A is to exceed his investment in the stock of company B by at least $20,000, determine how much he should invest in the stock of each company in order to maximize the return on his investment

Explanation / Answer

It's a classic two variables, two unknowns problem. You have the two variables, A (investment into company A) and B (investment into company B). You can find the two equations from the text.

A + B = 50000

You want to maximize B, so A will exceed B by exactly 20000 and no more. Thus:
A = B + 20000


You can substitute this value of A into the first equation:
(B + 20000) + B = 50000

and solve for B:
2B + 20000 = 50000
2B = 30000
B = 15000

Plug this value of B into either equation; let's choose the second one:
A = (15000) + 20000
A = 35000

Then check your work by seeing if these values of A and B work for the first equation too:

A + B = 50000
(35000) + (15000) = 50000
50000 = 50000
Yes.

A = 35000, B = 15000.

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