10 13 16 9 4 7 9 3 7 1 3. RDB Financial Company is planning to finance $100,000,000 various investments. Given below are the types of loans with its corresponding return and risk. Any unused money goes into a savings account with no risk and 3% return. RDB Company needs to allocate the money to the different types of investments so as to maximize the average return per dollar and have an average risk of no more than 5 (all averages and fractions taken over the invested money (not over the saving account)). RDB Company must also invest at least 20% in commercial loans; and the amount in second mortgages and personal loans combined should be not higher than the amount in first mortgages. Investment Return (%) Risk (1 = best) First Mortgages Second Mortgages Personal Loans Commercial Loans Government Securities 4. A store is opening a new department with a storage area of 20,000 ft?. Management considers 4 products for display. Product A: costs P60, sells for P90, and requires 28 square feet per unit of storage. Product B: costs P120, sells for P180, and requires 40 square feet per unit of storage. Product C: costs P240, sells for P345, and requires 34 square feet per unit of storage. Product D: costs P300, sells for P599, and requires 60 square feet per unit of storage. It is required that at least 15 units of each product be on display. The company's objective is profit maximization. Formulate the LP model that will determine how many units of each product should be on display if the company has P900,000 available for purchasing the product. 5. A newly-elected mayor has made high school education one of his priority programs. As a result, he has commissioned the building of 3 public high schools in his municipality. For geographical purposes of monitoring, he has divided his municipality into 5 areas: Zone 1, Zone 2, Zone 3, Zone 4 and Zone 5. He is building the schools only in areas Zone 2, Zone 3 and Zone 5 because of limited funds. To encourage students to go to school, he plans to provide school buses that will ease student travel. The table below presents the number of high school students in each geographic area and the distance in kilometers) of each area to a school. Each school has a capacity of 1000 students. Set up the objective and constraint functions that will minimize the total number of student kilometers traveled. Distance to school (km) No. of Students Area zone 1 zone 2 zone 3 zone 4 zone 5 zone 2 6 5 2 9 15 zone 3 9 7 4 0 zone 5 7 15 9 7 12 800 600 200 900 500 10 13 16 9 4 7 9 3 7 1 3. RDB Financial Company is planning to finance $100,000,000 various investments. Given below are the types of loans with its corresponding return and risk. Any unused money goes into a savings account with no risk and 3% return. RDB Company needs to allocate the money to the different types of investments so as to maximize the average return per dollar and have an average risk of no more than 5 (all averages and fractions taken over the invested money (not over the saving account)). RDB Company must also invest at least 20% in commercial loans; and the amount in second mortgages and personal loans combined should be not higher than the amount in first mortgages. Investment Return (%) Risk (1 = best) First Mortgages Second Mortgages Personal Loans Commercial Loans Government Securities 4. A store is opening a new department with a storage area of 20,000 ft?. Management considers 4 products for display. Product A: costs P60, sells for P90, and requires 28 square feet per unit of storage. Product B: costs P120, sells for P180, and requires 40 square feet per unit of storage. Product C: costs P240, sells for P345, and requires 34 square feet per unit of storage. Product D: costs P300, sells for P599, and requires 60 square feet per unit of storage. It is required that at least 15 units of each product be on display. The company's objective is profit maximization. Formulate the LP model that will determine how many units of each product should be on display if the company has P900,000 available for purchasing the product. 5. A newly-elected mayor has made high school education one of his priority programs. As a result, he has commissioned the building of 3 public high schools in his municipality. For geographical purposes of monitoring, he has divided his municipality into 5 areas: Zone 1, Zone 2, Zone 3, Zone 4 and Zone 5. He is building the schools only in areas Zone 2, Zone 3 and Zone 5 because of limited funds. To encourage students to go to school, he plans to provide school buses that will ease student travel. The table below presents the number of high school students in each geographic area and the distance in kilometers) of each area to a school. Each school has a capacity of 1000 students. Set up the objective and constraint functions that will minimize the total number of student kilometers traveled. Distance to school (km) No. of Students Area zone 1 zone 2 zone 3 zone 4 zone 5 zone 2 6 5 2 9 15 zone 3 9 7 4 0 zone 5 7 15 9 7 12 800 600 200 900 500