Exam 8: Nonlinear Programming Evolutionary Optimization

When using the GRG algorithm to solve NLPs one should try multiple starting points because

An investor wants to determine how much interest he must earn to be able to make the payments on a 10-year mortgage which has increasing annual payments. The problem is summarized in the accompanying spreadsheet. The investor has enough money to make an initial investment of $12,000 and hopes he can earn 18% on his investments. He would like to know how low his annual return can be and still allow him to make his payments from interest income. What formulas should go in cells B7:F7 of the spreadsheet for this problem?

An office supply company is attempting to determine the order quantity for Mt. White fountain pens which are sold to local executives. Annual demand is 5,000 units and each pen costs the store $50. It costs $75 to place an order and the inventory carrying cost rate is 30% of the value of the item. ​ Formulate the objective function for this problem. Let Q indicate the order quantity.

The optimal trade-off between risk and return for a given portfolio problem can be summarized by the

In solving the NLP problem, Solver found a degenerate model. This means that:

Nonzero reduced gradient values indicate the exact impact on the objective function value of large changes in the value of a given variable

How many local maximum solutions are there on this graph of a function? Mark their locations on the graph. ​

What is the search path for the following feasible solution space? The dashed line represents the objective function and the objective is to maximize the value of the objective function. ​ ​

A company wants to locate a new warehouse to minimize the distance travelled by its delivery trucks. It has four stores and their coordinates are listed in the accompanying spreadsheet. What formulas should go in cells D4:D9 of the spreadsheet for this problem?

An investor is developing a portfolio of stocks. She has identified 3 stocks in which to invest. She wants to earn at least 11% return but with minimum risk. Let: P_i = proportion of total funds invested in i, i = A, B, C The NLP for this problem is: What formulas should go in cells G4:J14 of the spreadsheet for this problem? NOTE: Formulas are not required in all of these cells. ​

The global optimum solution to a nonlinear programming problems (NLP), in which the objective function must be maximized, is:

The total annual cost for the economic order quantity model is

Exhibit 8.1 The following questions pertain to the problem and spreadsheet below. A company makes products A and B from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. A unit of A costs 25 to make and demand is estimated to be 20 − .10 * Price of A. A unit of B costs 18 to make and demand is estimated to be 30 − .07 * Price of B. The utilization of labor and materials and the available quantity of resources is shown in the table. A reasonable price for the products is between 100 and 200. Let X₁ = demand for As and X₂ = demand for Bs. Let P₁ = price for As and P₂ = price for Bs -Refer to Exhibit 8.1. What formula is used in cell B7 of the spreadsheet for this problem?

An investor wants to determine how much interest he must earn to be able to make the payments on a 10-year mortgage which has increasing annual payments. The problem is summarized in the accompanying spreadsheet. The investor has enough money to make an initial investment of $9,000 and hopes he can earn 12%, compounded quarterly, on his investments. He would like to know how low his annual return can be and still allow him to make his payments from interest income. What formula goes in cell C7 of the spreadsheet?

An investor wants to determine how much interest he must earn to be able to make the payments on a 10-year mortgage which has increasing annual payments. The problem is summarized in the accompanying spreadsheet. The investor has enough money to make an initial investment of $12,000 and hopes he can earn 18% on his investments. He would like to know how low his annual return can be and still allow him to make his payments from interest income. If the Analytic Solver Platform is used, which are the Objective, Variables and Constraint cells in the spreadsheet for this problem?

In solving the NLP problem, Solver produced a message "Solver has converged to the current solution. All constraints are satisfied." This means that:

A company wants to locate a new warehouse to minimize the distance travelled by its delivery trucks. It has four stores and their coordinates are listed in the below. Formulate the objective function for this problem. Let X and Y represent the X, Y coordinates of the new warehouse.

NLP problems which have slack in all the constraints

A company wants to locate a new warehouse to minimize the distance traveled by its delivery trucks. It has four stores and their coordinates are listed in the accompanying spreadsheet. What formula goes in cell D9 of the spreadsheet?

Exhibit 8.2 The following questions pertain to the problem and spreadsheet below. A construction company just purchased a 300 × 300 foot lot upon which they plan to build an office building. They need at least 60,000 ft² of office floor space. Zoning regulations require each floor be 10 feet high and the building not exceed 65 ft in height. Further, parking space must equal at least 30% of the total floor space available. The company's cost accountant uses a 60% factor of the building height and a 1% factor of any story's floor area to calculate the total building cost (in millions of dollars). The following is the NLP formulation for the problem. The spreadsheet implementation of this formulation applies to the following questions. -Refer to Exhibit 8.2. The company wishes to have a relatively square building. Thus, they wish neither the building length nor the building width exceed the other by more than 25%. Add constraint(s) to enforce this design constraint.