Hong Securities has $300,000 to invest in four stocks and three bonds.X₁, X₂, X₃, and X₄ denote the amounts invested in each of the stocks, and Y₁, Y₂, and Y₃ equal the amounts invested in each of the three bonds.Which of the following shows that at least 40% of the investment in stocks must be in stock 1? A)X₁ $\ge$ 120,000 B)X₁ - .4X₂ -.4X₃ - .4X₄ $\ge$ 0 C).6X₁ - .4X₂ - .4X₃ - .4X₄ $\ge$ 0 D)X₁ $\ge$ .4(X₂ + X₃ + X₄+ Y₁ + Y₂ + Y₃)

Question

Quizplus · Accepted Answer

We want to show that at least 40% of the investment in stocks must be in stock 1. Let's assume that the total investment in stocks is S and the investment in stock 1 is X. We know that S + Y₁ + Y₂ + Y₃ = $300,000 And we want to show that X/S >= 0.4 or X >= 0.4S From the given options, option C satisfies this condition: 0.6X₁ - 0.4X₂ - 0.4X₃ - 0.4X₄ >= 0 Multiplying by 5/3, we get: X₁ - 0.67(S - X₁) >= 0 Simplifying, 1.67X₁ - 0.67S >= 0 X₁ >= 0.4S Therefore, at least 40% of the investment in stocks must be in stock 1.

Hong Securities Has $300,000 to Invest in Four Stocks and Three