TradingCo wants to invest at most $10,000 in 2021. Two investment options are proposed: KTS and DB, with annual yields of 20% and 10% respectively. Based on market research, TradingCo wishes to limit the amount invested in KTS to no more than 60% of the total investment.

Let X₁ be KTS

Let X₂ be DB

Max Z: Z = 0.2X₁ + 0.1X₂

X₁ + X₂ <= $10,000 (Constrant 1)

0.4X₁ - 0.6X₂ <=0 (Constrant 2)

X₁,X₂ >=0 (non-negative constrants)

Suppose that TradingCo imposes one more restriction: investment in DB should be at leastatimes the investment in KTS where ais a non-negative constant. Find the optimal solution to the problem and discuss how the value of a would affect TradingCo's best investment decision and annual yield. (Use the graphical method and solve for the optimal solution in terms of a)