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mathematics
calculus

Questions and Answers of Calculus

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.
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
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
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
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
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
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
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
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
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
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
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,
(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
(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
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
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
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
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%
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
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
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 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
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
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
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
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
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
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
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
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
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,
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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