Natasano has at most $50,000 to invest in the common stocks of two companies. He

Question

Natasano has at most $50,000 to invest in the common stocks of two companies. He estimates that an investment in company A will yield a return of 10%,wheras an investment in company B,which he feels is a riskier investment, will yield a return of 20%. If he decides that his investment in the stock of company A is to exceed his investment in the stock in 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

let x=a
let y =b

Maximize z=.1x+.2y

subject to
x,y>+0
x+y<=50000
x-y>=20000

graph the system,find the corner points

(20000,0)
(50000,0)
(35000,15000)

he should invest 35000 in A
he should invest 15000 in B
to maximize his profit at $6500

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