Exam 8: Nonlinear Programming Evolutionary Optimization

In solving the NLP problem, Solver produced a message "Solver found a solution. All constraints and optimality conditions are satisfied." This means that Solver found:

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 product A costs 25 to make and demand is estimated to be 20 − .10 * Price of A. A unit of product 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. The objective function for this problem is?

The Analytic Solver Platform solution strategy for NLP problems is the GRG method. What does GRG stand for?

In the GRG algorithm the initial solution is called the

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 constraint must be entered in the Analytic Solver Platform (ASP) task pane?

An investor is developing a portfolio of stocks. She has identified 3 stocks to invest in. She wants to earn at least 5% return but with minimum risk. The problem data is given in the following Excel spreadsheet. What formula should be entered in cell G4 of the Excel spreadsheet? ​

Calculate the annual inventory costs for the following data.

The optimal solution to a NLP problem can occur at a(n) I. Corner point. II) Interior point.

Which point or points are global optima in this diagram? The dashed line represents the objective function and the objective is to maximize the value of the objective function. ​ ​

How much are additional units of Labor worth based on the following sensitivity report?

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 D12 of the spreadsheet for this problem?

Find the maximum solution on this graph of a function starting from X = 12. Mark its location on the graph. ​

​A given local optimal solution is also a global optimal solution to a NLP problem

The process of formulating an NLP problem is virtually the same as formulating an LP problem

The main difference between linear (LP) and nonlinear programming problems (NLP) is that

This selection of the initial feasible solution, often referred to as starting point, has no impact on the determination of the optimal solution to the NLP problem

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. What formula would you place in cell D13 to calculate total cost?

The Lagrange Multiplier is similar to which of these terms from linear programming?

A nonzero reduced gradient value indicates the approximate impact

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 30 to make and demand is estimated to be 50 − .09 * Price of A. A unit of B costs 20 to make and demand is estimated to be 30 − .14 * 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 90 and 140. Let X₁ = demand for As and X₂ = demand for Bs. Let P₁ = price for As and P₂ = price for Bs. Formulate the NLP for this company