For Example, construct a trade-off curve between the chosen portfolio’s expected return and variance. This is often called the efficient frontier.
Step 11 of 3
We have two objectives, maximize expected return and minimize variance. These objectives are given by the formulas
We have the restrains:
If we want to maximize expected return we obtain the solution
If we want to minimize variance we obtain the solution
Adding a restraint for we obtain the following values for the trade-off curve:
Bellow we show a graph of this trade-off curve.
Recommended textbook solutions
Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3. A desk contributes $40 to profit, and a chair contributes$25. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. If 20 units of wood are available, formulate an LP to maximize Furnco’s profit. Then graphically solve the LP.
Farmer Jones must determine how many acres of com and wheat to plant this year. An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week. An acre of corn yields 10 bushels of corn and requires 4 hours of labor per week. All wheat can be sold at $4 a bushel, and all com can be sold at$3 a bushel. Seven acres of land and 40 hours per week of labor are available. Government regulations requite that at least 30 bushels of corn be produced during the current year. Let x1 = number of acres of corn planted, and x2 = number of acres of wheat planted. Using these decision variables, formulate an LP whose solution will tell Farmer Jones how to maximize the total revenue from wheat and corn.
During each 4-hour period, the Smalltown police force requires the following number of on-duty police officers 12 midnight to 4 a.m. — 8; 4 to 8 a.m. —7; 8 a.m. to 12 noon—6; 12 noon to 4 p.m. —6; 4 to 8 p.m.—5; 8 p.m. to 12 midnight—4. Each police officer works two consecutive 4-hour shifts Formulate an LP that can be used to minimize the number of police officers needed to meet Smalltown’s daily requirements
Graphically solve Problem. Problem Truckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes $300 to profit; each Type 2 truck contributes$500. formulate an LP that will maximize Truckco’s profit.