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Exam 10: Integer Programming,goal Programming,and Nonlinear Programming

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Question 1

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Unfortunately,goal programming,while able to handle multiple objectives,is unable to prioritize these objectives.

A) True
B) False

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Question 2

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In an integer programming problem,if it is desired to have variable X be exactly twice the value of variable Y,the constraint would be written

A) 2X + Y = 0.
B) X + 2Y = 0.
C) 2X - Y = 0.
D) X - 2Y = 0.
E) None of the above

F) B) and C)
G) D) and E)

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Question 3

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In a goal programming problem with two goals at the same priority level,all the deviational variables are equal to zero in the optimal solution.This means

An integer programming (minimization) problem was first solved as a linear programming problem,and the objective function value (cost) was $253.67.The two decision variables (X,Y) in the problem had values of X = 12.45 and Y = 32.75.If there is a single optimal solution,which of the following must be true for the optimal integer solution to this problem?

In goal programming,the deviational variables have the same objective function coefficients as the surplus and slack variables in a normal linear program.

A bakery produces muffins and doughnuts.Let x₁ be the number of doughnuts produced and x₂ be the number of muffins produced.The profit function for the bakery is expressed by the following equation: profit = 4x₁ + 2x₂ + 0.3x₁² + 0.4x₂².The bakery has the capacity to produce 800 units of muffins and doughnuts combined and it takes 30 minutes to produce 100 muffins and 20 minutes to produce 100 doughnuts.There is a total of 4 hours available for baking time.There must be at least 200 units of muffins and at least 200 units of doughnuts produced.How many doughnuts and muffins should the bakery produce in order to maximize profit?

The concept of a local optimum is affiliated with which of the following?

Unfortunately,multiple goals in goal programming are not able to be prioritized and solved.

A capital budgeting problem involving the selection of possible projects under budget constraints is solved by which of the following?

As part of a larger problem,you are trying to determine whether or not to open a plant with a capacity of 10,000 units (using binary variable Y) .You also define X as the number of units (if any) produced at that plant.How will you ensure that Y will equal 1 if the plant is open?

Data Equipment Inc.produces two models of a retail price scanner,a sophisticated model that can be networked to a central processing unit and a stand-alone model for small retailers.The major limitations of the manufacturing of these two products are labor and material capacities.The following table summarizes the usages and capacities associated with each product. The typical LP formulation for this problem is: Maximize $160 X₁ + $95 X₂ Subject to: 8 X₁ + 5 X₂ ≤ 800 20 X₁ + 7 X₂ ≤ 1500 X₁,X₂ ≥ 0 However,the management of DEI has prioritized several goals that are to be attained by manufacturing: (1)Since the labor situation at the plant is uneasy (i.e. ,there are rumors that a local union is considering an organizing campaign),management wants to assure full employment of all its employees. (2)Management has established a profit goal of $12,000 per day. (3)Due to the high prices of components from nonroutine suppliers,management wants to minimize the purchase of additional materials. Given the above additional information,set this up as a goal programming problem.

A goal programming problem had two goals (with no priorities assigned) .Goal number 1 was to achieve a cost of $3,600 and goal number 2 was to have no wasted material.The optimal solution to this problem resulted in a cost of $3,900 and no wasted material.What was the value for the objective function for this goal programming problem?

Table 10-3 A company has decided to use 0−1 integer programming to help make some investment decisions.There are three possible investment alternatives from which to choose,but if it is decided that a particular alternative is to be selected,the entire cost of that alternative will be incurred (i.e. ,it is impossible to build one-half of a factory) .The integer programming model is as follows: Maximize 5000 X₁ + 7000X₂ + 9000X₃ Subject to: X₁ + X₂ + X₃ ≤ 2 Constraint 1 -X₁ + X₂ ≤ 0 Constraint 2 25,000 X₁ + 32,000 X₂ + 29,000 X₃ ≤ 62,000 (budget limit) 16 X₁ + 14 X₂ + 19 X₃ ≤ 36 (resource limitation) all variables = 0 or 1 where X₁ = 1 if alternative 1 is selected,0 otherwise X₂ = 1 if alternative 2 is selected,0 otherwise X₃ = 1 if alternative 3 is selected,0 otherwise Solution x₁ = 1,x₂ = 0,x₃ = 1,objective value = 14,000. -Table 10-3 presents an integer programming problem.What is the meaning of Constraint 1?

Data Equipment Inc.produces two models of a retail price scanner,a sophisticated model that can be networked to a central processing unit and a stand-alone model for small retailers.The major limitations of the manufacturing of these two products are labor and material capacities.The following table summarizes the usages and capacities associated with each product. The typical LP formulation for this problem is: Maximize P = $160 X₁ + $95 X₂ Subject to: 8 X₁ + 5 X₂ ≤ 800 20 X₁ + 7 X₂ ≤ 1500 X₁,X₂ ≥ 0 However,the management of DEI has prioritized several goals that are to be attained by manufacturing: (1)Management had decided to severely limit overtime. (2)Management has established a profit goal of $15,000 per day. (3)Due to the difficulty of obtaining components from non-routine suppliers,management wants to end production with at least 50 units of each component remaining in stock. (4)Management also believes that they should produce at least 30 units of the network model. Given the above additional information,set this up as a goal programming problem.

What is mixed integer programming?

A model containing a linear objective function and requiring that one or more of the decision variables take on an integer value in the final solution is called

Assignment problems solved previously by linear programming techniques are also examples of

In goal programming,our goal is to drive the deviational variables in the objective function as close to zero as possible.

Johnny's apple shop sells home-made apple pies and freshly squeezed apple juice.Each apple pie requires 2 apples,and 1 apple yields 4 ounces of juice.Customer's use a self-service dispenser to pour apple juice in a container and are charged by the ounce at a rate of $0.50 per ounce.The contribution to profit of the apple pie,factoring in the apples and remaining ingredients are $2 per pie,and the contribution to profit of freshly squeezed apple juice if $0.20 per ounce.In a given day,there must be at least 100 ounces of apple juice produced and at least 10 apple pies.The company has a supply of 60 apples per day.Formulate this problem as a mixed integer program.Apple pies must be produced in whole quantities,but any positive value is positive for juice production.

Table 10-4 -Table 10-4 represents a solution to a goal programming problem.There are three goals (each represented by a constraint) .Which of the goals is assigned the highest priority?