Exam 4: Linear Programming: Modeling Examples

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. -An appropriate part of the model would be:

Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is:

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week. The table below shows relevant manufacturing information: -Write the constraints for the total number of shirts of each style produced.

An unbalanced transportation model must have at least one ________ constraint.

Blending problems usually require algebraic manipulation in order to write the LP in "standard form."

________ types of linear programming problems often result in fractional relations between variables which must be eliminated.

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________.

Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How much oil-based and water-based paint should the Quickbrush make?

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. -This represents what type of linear programming application?

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week. The table below shows relevant manufacturing information: -Write the constraints for the fabric requirements.

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Leghorn Cochin Buff Orpington Eggs/week 5 2 4.5 Plumage 3 9 6 Temperment 2 8 5 Fertilizer 3 2 4 Appetite 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. -What is a full set of constraints if the farmer wants this flock to produce less than 100 decibels of noise and more than 5 pounds of fertilizer, consume less than 10 pounds of layer pellets, and achieve a total plumage score of at least 75?

Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter.

Investment problems maximize ________.

In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit.

Data envelopment analysis indicates which type of service unit makes the highest profit.

When using a linear programming model to solve the diet problem, the objective is generally to maximize profit.

Data envelopment analysis problems are usually maximization problems.

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Leghorn Cochin Buff Orpington Eggs/week 5 2 4.5 Plumage 3 9 6 Temperment 2 8 5 Fertilizer 3 2 4 Appetite 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. -How should the objective function read?

Fractional relationships among variables are considered standard form in a blending problem.

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. -The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint?