Day Trader wants to invest a sum of money that would generate an annually yield of at least $10,000. Two stock groups are available: blue chips and high tech, with average an annual yields of 10% and 25%, respectively. Though high tech stocks provides higher yield, they are more risky and Trader wants to limit the amount invested in these stocks to no more that 60% of the total investment. What is the minimum amount Trader should invest in each stock group to accomplish the investment goal?

a) Write a linear programming model for this problem.

b) Solve the model by using LINGO software.

c) Determine the optimality ranges and feasibility ranges

2. Develop the Branch and Bound tree for the following problem. For convenience, always select x1 as the branching variable at node 0.

Maximize z= 2x₁ + 3x₂

subject to 5x₁ + 7x₂ ? 35

4x_{1 +} 9x₂ ? 36

x₁ + x₂ ? 0