Please solve the following Operational Research problem. Please show all work and please do all parts thank you.

Problem 5.(30 points.) An individual wishes to invest $5000 over the next year in two types of investment: Investment A yields 5% and investment B yields 8%. Market research recommends an allocation of at least 25% in A and at most 50% in B. Moreover, investment in A should be at least half the investment in B. How should the fund be allocated to the two investments? (Build the mathematical model and find the optimal solution.) Solution