Exam 8: Nonlinear Programming and Evolutionary Optimization

A company has collected the following inventory data for an item. What is the total annual cost for this item?

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

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 values would you enter in the Risk Solver Platform (RSP) task pane for the above Excel spreadsheet? Objective Cell: Variables Cells: Constraints Cells:

The total annual cost for the economic order quantity model is

Which point or points are local 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?

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

The optimal solution to a LP problem is always at

An investor is developing a portfolio of stocks. She has identified 3 stocks in which to invest. She wants to earn at least 5% return but with minimum risk. Let: P_i = proportion of total funds invested in stock i $\sigma$ _i² = variance of stock i $\sigma$ _ij = covariance between stocks i and j.R_i = average return on stock i What is the objective function for the NLP formulation of this problem?

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

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. The average return for the stocks is: The covariance matrix for the stocks is: Let: P_i = proportion of total funds invested in i, i = A, B, C Formulate the NLP for this problem.

The optimal trade-off between risk and return for a given portfolio problem can be summarized by 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 $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 Risk Solver Platform (RSP) is used, which are the Objective, Variables and Constraint cells in the spreadsheet for this problem?

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 D4 of the spreadsheet?

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?

How much must the objective function coefficient of the variable X₂ increase before any X₂s are produced based on the following sensitivity report?

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?

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 B6 to calculate Total Lot Area?

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

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?