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Questions and Answers of Calculus

The King Trucking Company has an order for three products for delivery. The following table gives the particulars for the products.If the carrier can carry 6000 cu ft, can carry 11,000 lb, and is
A botanist can purchase plant food of four different types, I, II, III, and IV. Each food comes in the same size bag, and the following table summarizes the number of grams of each of three nutrients
In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If x1
Three different bacteria are cultured in one dish and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third
An irrigation system allows water to flow in the pattern shown in the figure below. Water flows into the system at A and exits at B, C, D, and E with the amounts shown. Using the fact that at each
An investment club has set a goal of earning 15% on the money they invest in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their
A trust account manager has $220,000 to be invested. The investment choices have current yields of 8%, 7%, and 10%. Suppose that the investment goal is to earn interest of $16,600, and risk factors
A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3
Each matrix is an augmented matrix representing a system of linear equations in x, y, and z. Use the Gauss-Jordan elimination method (see Gauss- Jordan elimination method box and Example 1) to find
1. If A is a 3 Ã— 3 matrix and B is its inverse, what does the product AB equal?2. Ifand Are C and D inverse matrices?
Find the inverse of matrix A and check it by calculating AA-1.1.2. 3. 4.
Find the inverse matrix for each matrix that has an inverse?1.2.3.4.
1. Find the inverse of2. Find the inverse of
The inverse of matrix A is given. Use the inverse of solve for X?1.Solve 2. Solve 3. Solve 4. Solve
Use the inverse found in Problem to solve
Use inverse matrices to solve each system of linear equations?1.2.3.4.
Use inverse matrices to find the solution of the systems of equations?1.2. 3. 4.
(a) Evaluate each determinant, and(b) Use the determinant to decide whether each matrix has an inverse. Use technology in Problems.1.2.3.4.
Use the code from the Application Preview and the given encoding matrix A to decode the given message.1. If the code matrix isdecode the message49, 59, 133, 161, 270, 327, 313, 3812. If the code
Find the inverse matrix for each matrix that has an inverse?1.2. 3. 4.
1. A product is made by only two competing companies. Suppose Company X retains two-thirds of its customers and loses one-third to Company Y each year, and Company Y retains three quarters of its
Medication A is given every 4 hours and medication B is given twice per day, and the ratio of the dosage of A to the dosage of B is always 5 to 8.(a) For patient I, the total intake of the two
The Ace Freight Company has an order for two products to be delivered to two stores of a company. The table gives information regarding the two products.(a) If truck A can carry 2350 cu ft and 23,000
One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman has $145,600 to invest and would like to have an income of $20,000 per year from her investments. How
A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centimeters of each solution should be mixed to obtain 25 cc of a 28% solution?
A manufacturer of table saws has three models, Deluxe, Premium, and Ultimate, which must be painted, assembled, and packaged for shipping. The table gives the number of hours required for each of
Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of
A trust account manager has $1,000,000 to be invested in three different accounts. The accounts pay 6%, 8%, and 10%, and the goal is to earn $86,000 with the amount invested at 10% equal to the sum
A company offers three mutual fund plans for its employees. Plan I consists of 4 blocks of common stock and 2 municipal bonds. Plan II consists of 8 blocks of common stock, 4 municipal bonds, and 6
Suppose that during the first 2 weeks of a controversial art exhibit, the daily number of visitors to the gallery turns out to be the sum of the numbers of visitors on the previous 3 days. We
Because a female bee comes from a fertilized egg and a male bee comes from an unfertilized egg, the number (nt+2) of ancestors of a male bee t + 2 generations before the present generation is the sum
The population of a colony of bacteria grows in such a way that the population size at anyhour t is the sum of the populations of the 3 previous hours. Suppose that the matrixdescribes the population
1. The following technology matrix for a simple economy describes the relationship of certain industries to each other in the production of 1 unit of product.(a) For each 100 units of manufactured
Suppose a primitive economy consists of two industries, farm products and farm machinery. Suppose also that its technology matrix isIf surpluses of 96 units of farm products and 8 units of farm
Suppose an economy has two industries, agriculture and minerals. Suppose further that the technology matrix for this economy is A.If surpluses of 60 agricultural units and 70 mineral units are
An economy is based on two industries: utilities and manufacturing. The technology matrix for these industries is A.If surpluses of 80 units of utilities output and 180 units of manufacturing are
A primitive economy has a mining industry and a fishing industry, with technology matrix A.If surpluses of 147 units of mining output and 26 units of fishing output are desired, find the gross
Suppose the economy of an underdeveloped country has an agricultural industry and an oil industry, with technology matrix A.(a) If surpluses of 0 units of agricultural products and 610 units of oil
Suppose a simple economy with only an agricultural industry and a steel industry has the following technology matrix.(a) If surpluses of 15 units of agricultural products and 35 units of steel are
One sector of an economy consists of a mining industry and a manufacturing industry, with technology matrix A.(a) Surpluses of 36 units of mining output and 278 units of manufacturing output are
An underdeveloped country has an agricultural industry and a manufacturing industry, with technology matrix A.(a) Surpluses of 8 units of agricultural products and 620 units of manufactured products
A simple economy has an electronic components industry and a computer industry. Each unit of electronic components output requires inputs of 0.3 unit of electronic components and 0.2 unit of
An economy has an agricultural industry and a textile industry. Each unit of agricultural output requires 0.4 unit of agricultural input and 0.1 unit of textiles input. Each unit of textiles output
A primitive economy consists of a fishing industry and an oil industry. A unit of fishing industry output requires 0.30 unit of fishing industry input and 0.35 unit of oil industry input. A unit of
An economy has a manufacturing industry and a banking industry. Each unit of manufacturing output requires inputs of 0.5 unit of manufacturing and 0.2 unit of banking. Each unit of banking output
Suppose the development department of a firm charges 10% of its total monthly costs to the promotional department, and the promotional department charges 5% of its total monthly costs to the
Suppose the shipping department of a firm charges 20% of its total monthly costs to the printing department and that the printing department charges 10% of its total monthly costs to the shipping
Suppose the engineering department of a firm charges 20% of its total monthly costs to the computer department, and the computer department charges 25% of its total monthly costs to the engineering
The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department.
Suppose that an economy has three industries, fishing, agriculture, and mining, and that matrix A is the technology matrix for this economy.If surpluses of 110 units of fishing output and 50 units
Suppose that an economy has the same technology matrix as the economy in Problem 27. If surpluses of 180 units of fishing output, 90 units of agricultural goods, and 40 units of mining goods are
Suppose that the economy of a small nation has an electronics industry, a steel industry, and an auto industry, with the following technology matrix.If the nation wishes to have surpluses of 100
The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and food; RM, raw materials; M, manufacturing; F, fuels
Suppose an economy has the same technology matrix as that in Problem 29. If surpluses of 540 units of electronics, 30 units of steel, and 140 autos are desired, find the gross production for each
Suppose that a simple economy has three industries, service, manufacturing, and agriculture, and that matrix A is the technology matrix for this economy.If surpluses of 24 units of service output, 62
Suppose that an economy has the same technology matrix as the economy in Problem 31. If surpluses of 14 units of manufactured goods and 104 units of agricultural goods are desired, find the gross
Suppose the technology matrix for a closed model of a simple economy is given byFind the gross productions for the industries. Problems refer to closed Leontief models?
Suppose the technology matrix for a closed model of a simple economy is given by matrix A. Find the gross productions for the industries.Problems refer to closed Leontief models?
Suppose the technology matrix for a closed model of a simple economy is given by matrix A. Find the gross productions for the industries.Problems refer to closed Leontief models?
Suppose the technology matrix for a closed model of an economy is given by matrix A. Find the gross productions for the industries.Problems refer to closed Leontief models?
A closed model for an economy has a manufacturing industry, utilities industry, and households industry. Each unit of manufacturing output uses 0.5 unit of manufacturing input, 0.4 unit of utilities
A closed model for an economy identifies government, the profit sector, the nonprofit sector, and households as its industries. Each unit of government output requires 0.3 unit of government input,
For the storage shed in Example 6, find the number of each primary assembly item required to fill an order for 24 sheds, 12 braces, and 96 bolts?
Card tables are made by joining 4 legs and a top using 4 bolts. The legs are each made from a steel rod. The top has a frame made from 4 steel rods. A cover and 4 special clamps that brace the top
A sawhorse is made from 2 pairs of legs and a top joined with 4 nails. The top is a 2 Ã— 4-in. board 3 ft long. Each pair of legs is made from two 2 Ã— 4-in. boards 3 ft long,
A log carrier has a body made from a 4-ft length of reinforced cloth having a patch on each side and a dowel slid through each end to act as handles. The parts-listing matrix for the log carrier is
Use the matrices below as needed to complete Problems.1. Find Î±12 in matrix A. 2. Find b23 in matrix B. 3. Which of the matrices, if any, are 3 Ã— 4? 4. Which of the
The reduced matrix for a system of equations is given.(a) Identify the type of solution for the system (unique solution, no solution, or infinitely many solutions). Explain your reasoning.(b) For
Solve each system using matrices?1.2. 3. 4.
1. Are D and G inverse matrices ifAndFind the inverse of each matrix.2.3.4.
Solve each system of equations by using inverse matrices.1.2. 3.
(a) Find the determinant of the matrix.(b) Use it to decide whether the matrix has an inverse.1.2.
The Burr Cabinet Company manufactures bookcases and filing cabinets at two plants, A and B. Matrix M gives the production for the two plants during June, and matrix N gives the production for July.
If the company sells its bookcases to wholesalers for $100 and its filing cabinets for $120, for which month was the value of production higher: (a) At plant A? (b) At plant B?
A small church choir is made up of men and women who wear choir robes in the sizes shown in matrix A.Matrix B contains the prices (in dollars) of new robes and hoods according to size. Use these
Two departments of a firm, A and B, need different amounts of the same products. The following table gives the amounts of the products needed by the two departments.These three products are supplied
Over the period of time 2006-2015, Maura's actual return (per dollar of stock) was 0.013469 per month, Ward's actual return was 0.013543 per month, and Goldsmith's actual return was 0.006504. Under
A woman has $50,000 to invest. She has decided to invest all of it by purchasing some shares of stock in each of three companies: a fast-food chain that sells for $50 per share and has an expected
A biologist is growing three different types of slugs (types A, B, and C) in the same laboratory environment. Each day, the slugs are given a nutrient mixture that contains three different
An airline company has three types of aircraft that carry three types of cargo. The payload of each type is summarized in the table below.(a) Suppose that on a given day the airline must move 1100
An economy has a shipping industry and an agricultural industry with technology matrix A.(a) Surpluses of 4720 tons of shipping output and 40 tons of agricultural output are desired. Find the gross
A simple economy has a shoe industry and a cattle industry. Each unit of shoe output requires inputs of 0.1 unit of shoes and 0.2 unit of cattle products. Each unit of cattle products output requires
A look at the industrial sector of an economy can be simplified to include three industries: the mining industry, the manufacturing industry, and the fuels industry. The technology matrix for this
Suppose a closed Leontief model for a nation's economy has the following technology matrix.Find the gross production of each industry?
Perform the indicated operations in Problems?1. A + B2. C - E 11.3. DT - I4. 3C
Graph each inequality.1. y ≤ 2x - 12. y ≥ 4x - 53. x/2 + y/4 < 1
Graph the solution of each system of inequalities.1.2. 3.
The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble
An experiment that involves learning in animals requires placing white mice and rabbits into separate, controlled environments, environment I and environment II. The maximum amount of time available
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
Apex Motors manufactures luxury cars and sport utility vehicles. The most likely customers are high-income men and women, and company managers want to initiate an advertising campaign targeting these
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 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 each 1-minute
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
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
The graph of the boundary equations for each system of inequalities is shown with that system. Locate the solution region and find the corners.1.2.
Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist).1. C = 9x + 10y2. C = 2x + 7y
Maximize f = 7x + 10y subject to 3x + y ≤ 9 3x + 2y ≤12 x + 2y ≤ 8 x ≥ 0, y ≥ 0 Find the indicated maximum or minimum value of the objective function in the linear programming problem. The

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