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Mathematical Applications for the Management Life and Social Sciences 11th edition Ronald J. Harshbarger, James J. Reynolds - Solutions

Minimize g = 100x + 22y subject to x + 3y ≥ 3 2x + 3y ≥ 5 2x + y ≥ 3 x ≥ 0, y ≥ 0 Find the indicated maximum or minimum value of the objective function in the linear programming problem. The feasible regions for these problems are found in the answers to Problems 19, 20, 23, and 24 in the
Minimize g = 12x + 8y subject to x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0 Find the indicated maximum or minimum value of the objective function in the linear programming problem. The feasible regions for these problems are found in the answers to Problems 19, 20, 23, and 24 in the
Maximize f = 3x + 4y subject to x + y ≤ 6 2x + y ≤ 10 y ≤ 4 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Maximize f = x + 3y subject to x + 4y ≤ 12 y ≤ 2 x + y ≤ 9 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Maximize f = 2x + 6y subject to x + y ≤ 7 2x + y ≤ 12 x + 3y ≤ 15 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Maximize f = 4x + 2y subject to x + 2y ≤ 20 x + y ≤ 12 4x + y ≤ 36 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Minimize g = 7x + 6y subject to 5x + 2y ≥ 16 3x + 7y ≥ 27 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Minimize g = 22x + 17y subject to 8x + 5y ≥ 100 12x + 25y ≥ 360 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Minimize g = 3x + y subject to 4x + y ≥ 11 3x + 2y ≥ 12 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Minimize g = 50x + 70y subject to 11x + 15y ≥ 225 x + 3y ≥ 27 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Maximize f = x + 2y subject to x + y ≥ 4 2x + y ≤ 8 y ≤ 4 Solve the above linear programming problem. Restrict x ≥ 0 and y ≥ 0.
Maximize f = 3x + 5y subject to 2x + 4y ≥ 8 3x + y ≤ 7 y ≤ 4 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Minimize g = 40x + 25y subject to x + y ≥ 100 - x + y ≤ 20 - 2x + 3y ≥ 30 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
Minimize g = 3x + 8y subject to 4x - 5y ≥50 - x + 2y ≥ 4 x + y ≤ 80 Solve the following linear programming problems. Restrict x ≥ 0 and y ≥ 0.
The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 12 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum
An experiment involving learning in animals requires placing white mice and rabbits into separate, controlled environments, environment I and environment II. The maximum amount of time available in environment I is 500 minutes, and the maximum amount of time available in environment II is 600
A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 4 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300
Sierra Wood Products manufactures two high-quality products, rockers and bookshelf units. Its profit is $30 per rocker and $42 per bookshelf unit. Next week's production will be constrained by two limited resources, labor and wood. The labor available next week is expected to be at most 930 hours,
A candidate wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and that each 1-minute spot on radio reaches 0.006 million. The candidate feels she must reach at least 2.16 million
In a hospital ward, the patients can be grouped into two general categories depending on their condition and the amount of solid foods they require in their diet. A combination of two diets is used for solid foods because they supply essential nutrients for recovery, but each diet has an amount of
Newjet, Inc. manufactures inkjet printers and laser printers. The company has the capacity to make 70 printers per day, and it has 120 hours of labor per day available. It takes 1 hour to make an inkjet printer and 3 hours to make a laser printer. The profits are $40 per inkjet printer and $60 per
At one of its factories, a jeans manufacturer makes two styles: #891 and #917. Each pair of style-891 takes 10 minutes to cut out and 20 minutes to assemble and finish. Each pair of style- 917 takes 10 minutes to cut out and 30 minutes to assemble and finish. The plant has enough workers to provide
A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these fish. Bass require 2 units of food A and 4 units of food B, and trout require 5 units of food A and 2 units of food B. If the owner has 800 units of each food, find the
In a zoo, there is a natural habitat containing several feeding areas. One of these areas serves as a feeding area for two species, I and II, and it is supplied each day with 120 pounds of food A, 110 pounds of food B, and 57 pounds of food C. Each individual of species I requires 5 lb of A, 5 lb
(a) If one more acre of land became available (for a total of 6001 acres), how would this change the co-op's planting strategy and its maximum profit?(b) Repeat part (a) if 8 more acres of land were available.(c) Based on parts (a) and (b), what is the profit value of each additional acre of land?
(a) If one more gallon of fertilizer/herbicide became available (for a total of 40,501 gallons), how would this change the co-op's planting strategy and its maximum profit?(b) Repeat part (a) if 8 more gallons of fertilizer/ herbicide were available.(c) Based on parts (a) and (b), what is the
Two factories produce three different types of kitchen appliances. The following table summarizes the production capacity, the number of each type of appliance ordered, and the daily operating costs for the factories. How many days should each factory operate to fill the orders at minimum cost?
In a laboratory experiment, two separate foods are given to experimental animals. Each food contains essential ingredients, A and B, for which the animals have a minimum requirement, and each food also has an ingredient C, which can be harmful to the animals. The following table summarizes this
The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of standard drapes per day. At location II, it can make 20 pairs of deluxe, 50 pairs of better, and 6 pairs of
Two foods contain only proteins, carbohydrates, and fats. Food A costs $1 per pound and contains 30% protein and 50% carbohydrates. Food B costs $1.50 per pound and contains 20% protein and 75% carbohydrates. What combination of these two foods provides at least 1 pound of protein, 2 1/2 pounds of
A sausage company makes two different kinds of hot dogs, regular and all beef. Each pound of all-beef hot dogs requires 0.75 lb of beef and 0.2 lb of spices, and each pound of regular hot dogs requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 1020 lb of
A cereal manufacturer makes two different kinds of cereal, Senior Citizen's Feast and Kids Go. Each pound of Senior Citizen's Feast requires 0.6 lb of wheat and 0.2 lb of vitamin-enriched syrup, and each pound of Kids Go requires 0.4 lb of wheat, 0.2 lb of sugar, and 0.2 lb of vitamin-enriched
TV Circuit has 30 large-screen televisions in a warehouse in Erie and 60 large-screen televisions in a warehouse in Pittsburgh. Thirty-five are needed in a store in Blairsville, and 40 are needed in a store in Youngstown. It costs $18 to ship from Pittsburgh to Blairsville and $22 to ship from
A contractor builds two types of homes. The Carolina requires one lot, $160,000 capital, and 160 worker-days of labor, whereas the Savannah requires one lot, $240,000 capital, and 160 worker-days of labor. The contractor owns 300 lots and has $48,000,000 available capital and 43,200 worker-days of
A bank has two types of branches. A satellite branch employs 3 people, requires $100,000 to construct and open, and generates an average daily revenue of $10,000. A full-service branch employs 6 people, requires $140,000 to construct and open, and generates an average daily revenue of $18,000. The
A company manufactures two different sizes of boat lifts. Each size requires some time in the welding and assembly department and sometime in the parts and packaging department. The smaller lift requires ¾ hour in welding and assembly and 1 2/3 hours in parts and packaging. The larger lift
The graph of the feasible region is shown. Find the corners of each feasible region, and then find the maximum and minimum of the given objective function (if they exist).f = 3x + 2y
Maximize f = 30x + 50y subject to x + 2y ≤48 x + y ≤ 30 2x + y ≤ 50 x ≥ 0, y ≥0 Find the indicated maximum or minimum value of the objective function in the linear programming problem.
1. Convert the constraint inequalities 3x + 5y ≤ 15 and 3x + 6y ≤ 20 to equations containing slack variables. 2. Convert the constraint inequalities 2x + y ≤ 4 and 3x + 2y ≤ 8 to equations containing slack variables.
A simplex matrix for a standard maximization problem is given.(a) Write the values of all the variables (use x1, x2, x3, . . . and s1, s2, s3, . . .) and of the objective function f.(b) Indicate whether or not the solution from part (a) Is complete (optimal).(c) If the solution is not complete,
Maximize f = 3x + 10y subject to 14x + 7y ≤ 35 5x + 5y ≤ 50 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = 7x + 10y subject to 14x + 14y ≤ 98 8x + 10y ≤ 100 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = 2x + 3y subject to x + 2y ≤ 10 x + y ≤ 7 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = 5x + 30y subject to 2x + 10y ≤ 96 x + 10y ≤ 90 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = 2x + y subject to - x + y ≤ 2 x + 2y ≤ 10 3x + y ≤ 15 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = 2x + 6y subject to 2x + 5y ≤ 30 x + 5y ≤ 25 x + y ≤ 11 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = 7x + 10y + 4z subject to 3x + 5y + 4z ≤ 30 3x + 2y ≤ 4 x + 2y ≤ 8 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = 20x + 12y + 12z subject to x + z ≤ 40 x + y ≤ 30 y + z ≤ 40 Use the simplex method to maximize the given functions. Assume all variables are nonnegative.
Maximize f = x + 3y + z subject to x + 4y ≤ 12 3x + 6y + 4z ≤ 48 y + z ≤ 8 Use Excel to solve each linear programming problem.
Maximize f = 64x + 36y + 38z subject to 4x + 2y + 2z ≤ 40 8x + 10y + 5z ≤ 90 4x + 4y + 3z ≤ 30 Use Excel to solve each linear programming problem.
Maximize f = 24x1 + 30x2 + 18x3 + 18x4 subject to 12x1 + 16x2 + 20x3 + 8x4 ≤ 880 5x1 + 10x2 + 10x3 + 5x4 ≤ 460 10x1 - 5x2 + 8x3 + 5x4 ≤ 280 Use Excel to solve each linear programming problem.
Set up the simplex matrix used to solve each linear programming problem. Assume all variables are nonnegative. 1. Maximize f = 3x + 7y subject to 2x + 5y ≤400 x + 2y ≤175 2. Maximize f = x + 3y subject to 5x + y ≤ 50 x + 2y ≤ 50 3. Maximize f = 2x + 5y + 2z subject to 2x + 7y + 9z ≤
Maximize f = 8x1 + 17x2 + 24x3 + 31x4 + 36x5 subject to x1 + x2 + 5x3 + 3x4 + 2x5 ≤ 5000 2x1 + x2 + 4x3 + 4x4 + 2x5 ≤ 6000 3x1 + x2 + 5x3 + 2x4 + 3x5 ≤ 7000 Use Excel to solve each linear programming problem.
A simplex matrix is given for which the associated maximization problem either has no solution or has multiple solutions. If there is no solution, explain how you know this. If there are multiple solutions, give one solution and explain how you would find another.1.2. 3. 4.
Maximize f = 3x + 2y subject to x - 10y ≤ 10 - x + y ≤ 40 Use the simplex method to maximize each function (whenever possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, find two of them.
Maximize f = 10x + 15y subject to - 5x + y ≤ 24 2x - 3y ≤ 9 Use the simplex method to maximize each function (whenever possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, find two of them.
Maximize f = 3x + 12y subject to 2x + y ≤ 120 x + 4y ≤ 200 Use the simplex method to maximize each function (whenever possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, find two of them.
Maximize f = 8x + 6y subject to 4x + 3y ≤ 24 10x + 9y ≤ 198 Use the simplex method to maximize each function (whenever possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, find two of them.
Newjet Inc. manufactures two types of printers, an inkjet printer and a laser printer. The company can make a total of 60 printers per day, and it has 120 labor-hours per day available. It takes 1 laborhour to make an inkjet printer and 3 labor-hours to make a laser printer. The profits are $40 per
A contractor builds two types of homes. The Carolina requires one lot, $160,000 capital, and 160 worker-days of labor, and the Savannah requires one lot, $240,000 capital, and 160 worker-days of labor. The contractor owns 300 lots and has $48,000,000 available capital and 43,200 worker-days of
At one of its factories, a jeans manufacturer makes two styles: #891 and #917. Each pair of style-891 takes 10 minutes to cut out and 20 minutes to assemble and finish. Each pair of style- 917 takes 10 minutes to cut out and 30 minutes to assemble and finish. The plant has enough workers to provide
A car rental agency has a budget of $1.8 million to purchase at most 100 new cars. The agency will purchase either subcompact cars at $15,000 each or mid-sized cars at $30,000 each. From past rental patterns, the agency decides to purchase at most 50 mid-sized cars and expects an annual profit of
Happy Valley Ice Cream Company is planning its production for next week. Demand for Happy Valley's premium and light ice creams continues to outpace the company's production capacities. Two resources used in ice cream production are in short supply for next week. The mixing machines will be
An experiment involves placing the males and females of a laboratory animal species in two separate controlled environments. There is a limited time available in these environments, and the experimenter wishes to maximize the number of animals subject to the constraints described.How many males and
A contractor builds three types of houses: the Aries, the Belfair, and the Wexford. Each house requires one lot, and the following table gives the number of labor-hours and the amount of capital needed for each type of house, as well as the profit on the sale of each house. There are 12 lots,
A medical clinic performs three types of medical tests that use the same machines. Tests A, B, and C take 15 minutes, 30 minutes, and 1 hour, respectively, with respective profits of $150, $250, and $500. The clinic has four machines available. One person is qualified to do test A, two to do test
A woman has a building with 26 one-bedroom apartments, 40 two-bedroom apartments, and 60 three-bedroom apartments available to rent to students. She has set the rent at $500 per month for the one-bedroom units, $800 per month for the two- bedroom units, and $1150 per month for the three-bedroom
Patio Iron makes wrought iron outdoor dining tables, chairs, and stools. Each table uses 8 feet of a standard width wrought iron, 4 hours of labor for cutting and assembly, and 2 hours of labor for detail and finishing work. Each chair uses 6 feet of the wrought iron, 2 hours of cutting and
Tire Corral has $6000 available per month for advertising. Newspaper ads cost $100 each and can occur a maximum of 21 times per month. Radio ads cost $300 each and can occur a maximum of 28 times per month at this price. Each newspaper ad reaches 6000 men over 20 years of age, and each radio ad
A bicycle manufacturer makes mountain bikes and road bikes. Each mountain bike requires 2 units of steel and 6 units of aluminum in its frame and 12 special components for the hub, sprocket, and gear assembly. Each road bike requires 5 units each of steel and aluminum for its frame and 5 of the
A firm has decided to discontinue production of an unprofitable product. This will create excess capacity, and the firm is considering one or more of three possible new products: A, B, and C. The available daily hours in the plant will be 477 hours in tool and die, 350 hours on the drill presses,
The Laposata Pasta Company has $12,000 available for advertising. The following table gives the costs per ad and the numbers of people exposed to its ads for three different media (with numbers in thousands).If the total available audience is 420,000, and if the company wishes to maximize the
At one of its factories, a manufacturer of televisions makes one or more of four models of HD units (without cases): a 20-in. LCD, a 42-in. LCD, a 42-in. plasma, and a 50-in. plasma. The assembly and testing time requirements for each model are shown in the following table, together with the
Conglomo Corporation is considering investing in other smaller companies, and it can purchase any fraction of each company. Each investment by Conglomo requires a partial payment now and a final payment 1 year from now. For each investment, the following table summarizes the amount of each payment
A simplex matrix is given in which the solution is complete. Identify the maximum value of f and a set of values of the variables that gives this maximum value.1.2. 3. 4.
Minimize g = 4y1 + 5y2 subject to5y1 + 2y2 ≥ 16y1 + 2y2 ≥ 8Complete the following.(a) Form the matrix associated with each given minimization problem and find its transpose.(b) Write the dual maximization problem. Be sure to rename the variables.
Minimize g = 2y1 + 5y2 subject to 4y1 + y2 ≥ 12 y1 + y2 ≥ 9 y1 + 3y2 ≥ 15 Write the dual maximization problem, and then solve both the primal and dual problems with the simplex method.
Minimize g = 8x + 7y + 12z subject to x + y + z ≥ 3 y + 2z ≥ 2 x ≥ 2 Use the simplex method.
Minimize g = 12y1 + 8y2 + 10y3 subject to y1 + 2y3 ≥ 10 y1 + y2 ≥ 12 2y1 + 2y2 + y3 ≥ 8 Use the simplex method.
Minimize g = 12y1 + 48y2 + 8y3 subject to y1 + 3y2 ≥ 1 4y1 ≥ 6y2 + y3 ≥ 3 4y2 + y3 ≥ 1 Use the simplex method.
Minimize g = 20x + 30y + 36z subject to x + 2y + 3z ≥ 48 2x + 2y + 3z ≥ 70 2x + 3y + 4z ≥ 96 Use the simplex method.
Maximize f = 40x1 + 20x2 subject to3x1 + 2x2 ≤ 120x1 + x2 ≤ 50A primal maximization problem is given.(a) Form the dual minimization problem.(b) Solve both the primal and dual problems with the simplex method.
Maximize f = 28x1 + 12x2 subject to7x1 + 12x2 ≤ 502x1 + 6x2 ≤ 100A primal maximization problem is given.(a) Form the dual minimization problem.(b) Solve both the primal and dual problems with the simplex method.
Minimize g = 40y1 + 90y2 + 30y3 subject to y1 + 2y2 + y3 ≥ 16 y1 + 5y2 + 2y3 ≥ 18 2y1 + 5y2 + 3y3 ≥ 38 Use Excel or some other technology.
Minimize w = 48y1 + 20y2 + 8y3 subject to 4y1 + 2y2 + y3 ≥ 30 12y1 + 4y2 + 3y3 ≥ 60 2y1 + 3y2 + y3 ≥ 40 Use Excel or some other technology.
Minimize g = 50y1 + 20y2 + 30y3 + 80y4 subject to 40y1 + 20y2 + 15y3 + 50y4 ≥ 50 3y1 + 2y2 + 5y4 ≥ 6 2y1 + 2y2 + 4y3 + 4y4 ≥ 10 2y1 + 4y2 + y3 + 5y4 ≥ 8 Use Excel or some other technology.
Minimize g = 3y1 + 2y2 subject to3y1 + y2 ≥ 63y1 + 4y2 ≥ 12Complete the following.(a) Form the matrix associated with each given minimization problem and find its transpose.(b) Write the dual maximization problem. Be sure to rename the variables.
Minimize g = 200y1 + 100y2 + 200y3 + 40y4 subject to 3y1 + 2y2 + y3 + y4 ≥ 88 2y1 + 2y2 + y3 ≥ 86 2y1 + 4y2 + y3 ≥100 5y1 + 5y2 + y3 ≥ 100 Use Excel or some other technology.
CDF Appliances has assembly plants in Atlanta and Fort Worth where it produces a variety of kitchen appliances, including a 12-cup coffee maker and a cappuccino machine. In each hour at the Atlanta plant, 160 of the coffee makers and 200 of the cappuccino machines can be assembled, and the hourly
Nekita Corporation assembles cell phones and smart phones at two different factories within the same city. During each hour at the first factory, 15 cell phones and 30 smart phones can be assembled at a cost of $100/hour. During each hour at the second factory, 10 cell phones and 60 smart phones
The Video Star Company makes two different models of DVD players, which are assembled on two different assembly lines. Line 1 can assemble 30 units of the Star model and 40 units of the Prostar model per hour, and line 2 can assemble 150 units of the Star model and 40 units of the Prostar model per
A pork producer is considering two types of feed that contain the necessary ingredients for the nutritional requirements for fattening hogs. Red Star Brand contains 9 units of ingredient A and 12 units of ingredient B, and Blue Chip Brand contains 15 units of ingredient A and 9 units of ingredient
A small company produces two products, I and II, at three facilities, A, B, and C. It has orders for 2000 of product I and 1200 of product II. The production capacities and costs per week to operate the three facilities are summarized in the following table.How many weeks should each facility
In a hospital ward, the patients can be grouped into two general categories depending on their conditions and the amounts of solid foods they require in their diet. A combination of two diets is used for solid foods because they supply essential nutrients for recovery, but each diet has an amount
Two factories produce three different types of kitchen appliances. The following table summarizes the production capacities, the numbers of each type of appliance ordered, and the daily operating costs for the factories. How many days should each factory operate to fill the orders at minimum cost?
In a laboratory experiment, two separate foods are given to experimental animals. Each food contains essential ingredients, A and B, for which the animals have minimum requirements, and each food also has an ingredient C, which can be harmful to the animals. The following table summarizes this
A political candidate wishes to use a combination of radio and TV advertisements in her campaign. Research has shown that each 1-minute spot on TV reaches 0.9 million people and that each 1-minute spot on radio reaches 0.6 million. The candidate feels she must reach 63 million people, and she must
Minimize g = 7y1 + 3y2 subject toy1 + 2y2 ≥ 30y1 + 4y2 ≥ 50Complete the following.(a) Form the matrix associated with each given minimization problem and find its transpose.(b) Write the dual maximization problem. Be sure to rename the variables.
The James MacGregor Mining Company owns three mines: I, II, and III. Three grades of ore, A, B, and C, are mined at these mines. For each grade of ore, the number of tons per week available from each mine and the number of tons per week required to fill orders are given in the following table.Find
DeTurris Office Supplies presently carries reams of printer paper in three different grades: recycled, satin white, and glossy white. Three wholesalers offer special purchase packages consisting of different numbers of reams of these three grades, as shown in the following table. DeTurris Office

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