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Exam 8: Nonlinear Programming Evolutionary Optimization

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Question 1

Multiple Choice

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The main difference between shadow prices and Lagrange multipliers is

A) the range of RHS values over which the Lagrange multipliers or the shadow prices remain valid
B) that shadow prices overestimate the impact of a small change in the RHS of the constraints on the objective function
C) that shadow prices underestimate the impact of a small change in the RHS of the constraints on the objective function
D) they are equivalent

Correct Answer

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A

Question 2

Multiple Choice

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In solving the NLP problem, Solver produced a message "Solver cannot improve the current solution. All constraints are satisfied." This means that Solver found:

A) a local optimal solution
B) a global optimal solution
C) the objective function changed very slowly for the last few iterations
D) a degenerate model

Correct Answer

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D

Question 3

Multiple Choice

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The straight line (Euclidean) distance between two points (X₁, Y₁) and (X₂, Y₂) is calculated as

An office supply company is attempting to determine the order quantity for laser printer toner cartridges which are sold to local businesses. Annual demand is 20,000 units and each cartridge costs the store $25. It costs $30 to place an order and the inventory carrying cost rate is 25% of the value of the item. The following spreadsheet has been set up to solve the problem. What formula goes in cell B11 in this problem?

An office supply company is attempting to determine the order quantity for laser printer toner cartridges which are sold to local businesses. Annual demand is 20,000 units and each cartridge costs the store $25. It costs $30 to place an order and the inventory carrying cost rate is 25% of the value of the item. The following spreadsheet has been set up to solve the problem. What constraint would you impose on this problem to ensure that at least one order is placed per year?

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 values would you enter in the Analytic Solver Platform task pane for the above Excel spreadsheet? ​ Objective Cell: ​ Variables Cells: ​ Constraints Cells:

​The solution procedure Solver uses to solve NLP problems is called the generalized reduced gradient (GRG) algorithm

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

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?

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 H11 of the Excel spreadsheet? ​

The Lagrange multipliers can be used to

The GRG and Simplex algorithms are similar in that

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 main difference between shadow prices and Lagrange multipliers involves the range of RHS values over which the shadow price or Lagrange multiplier remains valid

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

What is the straight line (Euclidean) distance between the points (5,7) and (1, 11) ?

A NLP problem can have nonlinear objective and a nonlinear constraints

The optimal solution to a LP problem is always at I. A corner point. II) An interior point III) The origin.

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 into cell B5 to calculate Total Floor Area?

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