2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed a questionnaire to measure each client’s risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the client as a moderate investor. Provident recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 240. a. Formulate a linear programming model to find the best investment strategy for this client. b. Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client? What is the annual return for the portfolio?
2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest.
Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%.
The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100.
Finally, Provident developed a questionnaire to measure each client’s risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the client as a moderate investor. Provident recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 240.
a. Formulate a linear programming model to find the best investment strategy for this client.
b. Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client? What is the annual return for the portfolio?
3. Atlas Fertz Corp. makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A kilogram of ingredient 1 contributes 150 grams of nitrogen and 90 grams of phosphate, while a kilogram of ingredient 2 contributes 30 grams of nitrogen, 90 grams of phosphate, and 15 grams of potassium. Ingredient 1 costs P300 per kilograms , and ingredient 2 costs P500 per kilogram. The company wants to know how many kilogram of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 600 grams of nitrogen, 1080 grams of phosphate, and 60 grams of potassium while minimizing cost.
a. Formulate the LP model for this problem.
b. Develop a spreadsheet model and solve using Excel Solver. What is the optimal solution?
Step by step
Solved in 2 steps with 4 images
3. Atlas Fertz Corp. makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A kilogram of ingredient 1 contributes 150 grams of nitrogen and 90 grams of phosphate, while a kilogram of ingredient 2 contributes 30 grams of nitrogen, 90 grams of phosphate, and 15 grams of potassium. Ingredient 1 costs P300 per kilograms , and ingredient 2 costs P500 per kilogram. The company wants to know how many kilogram of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 600 grams of nitrogen, 1080 grams of phosphate, and 60 grams of potassium while minimizing cost.
a. Formulate the LP model for this problem.
b. Develop a spreadsheet model and solve using Excel Solver. What is the optimal solution?
by Bartleby Expert