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

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

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.Formulate a nonlinear program representing the profit maximization problem for the bakery.

There is no general method for solving all nonlinear problems.

Which of the following functions is nonlinear?

A mathematical programming model that permits decision makers to set and prioritize multiple objective functions is called a

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?

Smalltime Investments Inc.is going to purchase new computers.There are ten employees, and the company would like one for each employee.The cost of the basic personal computer with monitor and disk drive is $2,000, while the deluxe version with VGA and advanced processor is $3,500.Due to internal politics, the number of deluxe computers should be less than half the number of regular computers, but at least three deluxe computers must be purchased.The budget is $27,000, although additional money could be used if it were deemed necessary.All of these are goals that the company has identified.Formulate this as a goal programming problem.

The following objective function is nonlinear: Max 5X + (1/8)Y - Z.

0-1 integer programming might be applicable to selecting the best gymnastics team to represent a country from among all identified teams.

A goal programming problem had two goals (with no priorities assigned).Goal number 1 was to achieve a profit of $3,600 and goal number 2 was to have no wasted material.The optimal solution to this problem resulted in a profit of $3,300 and no wasted material.What was the value for the objective function for this goal programming problem?

The following Maximize: 7X₁ + 3X₂ Subject to: 5X₁ + 7X₂ ≤ 27 4X₁ + X₂ ≤ 14 3X₁ - 2X₂ ≤ 9 X₁, X₂ ≥ 0 X₁ integer Represents a:

Johnny's apple shop sells homemade 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 is $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.What is the optimal solution? Apple pies must be produced in whole quantities, but any positive value is positive for juice production.

The transportation problem is a good example of a pure integer programming problem.

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

How many constraints are required to develop an integer solution to the haberdashery problem described in Table 10-9?

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

The constraint X₁ - X₂ ≤ 0 with 0 -1 integer programming allows for X₁ to be selected as part of the optimal solution only if X₂ is selected to be a part of the optimal solution, but not both.

Goal programming differs from linear programming in which of the following aspects?

How many constraints are required to develop an integer solution to the haberdashery problem described in Table 10-9?

In goal programming, if all the goals are achieved, then the value of the objective function will always be zero.