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mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

In Problems, graph the functions.y = 5x
In Problems, graph each inequality.-y/8 > 1/4
In Problems, 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 = 5x + 8y y 4x
Maximize f = 3x + 5y subject to the constraints determined by the shaded region shown in the figure. y 24 (8, 18) 16 8- + 8. 16 24
Following are three simplex matrices in various stages of the simplex method solution of a maximization problem.(a) Identify the matrix for which multiple solutions exist. Circle the pivot and
In Problems, graph each inequality.y ≥ 4x - 5
In, use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist).f = 5x + 2y у (0,6) 5 3 (1, 3) (2, 1) (4,
Graph the solution region for each of the following.(a) 3x - 5y ≤ 30(b) x > 2(c) 5y > 2x x + y>7 2y < 5x
In Problems, graph each inequality.x/2 + y/4 < 1
In, use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist).f = 4x + 5y y 7 (0, 6) 5 3 (2, 2) (4, 1)
In Problems, graph each inequality.x - y/3 < -2/3
Formulate the dual maximization problem associated with the following.Minimize g = 2y1 + 3y2 + 5y3 subject to3y1 + 5y2 + 3y3 ≥ 1004y1 + 6y2 + 3y3 ≥ 120y1 ≥ 0, y2 ≥ 0, y3 ≥ 0
In Problems, graph each inequality.0.4x ≥ 0.8
Find the maximum and minimum values of f = 5x + 2y (if they exist) subject to the constraints determined by the shaded region in the figure. y x+ y = 9 x + 3y = 15 4x + y = 12
Use graphical methods to minimize g = 3x + y subject to 5x - 4y ≤ 40, x + y ≥ 80, 2x - y ≥ 4, x ≥ 0, and y ≥ 0.
In Problems, a function and the graph of a feasible region are given. In each case, find both the maximum and minimum values of the function, if they exist, and the point at which each occurs.f = 7x
In Problems, 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).g = 2x + 3y 3x +
Express the following linear programming problem as a maximization problem with # constraints. Assume that x ≥ 0, y ≥ 0.Minimize g = 7x + 3y subject to
In Problems, complete both of the following.(a) State the given problem in a form from which the simplex matrix can be formed (that is, as a maximization problem with " constraints).(b) Form the
In Problems, a function and the graph of a feasible region are given. In each case, find both the maximum and minimum values of the function, if they exist, and the point at which each occurs.f = 9x
In Problems, 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).g = x + 3y 3x +
The final simplex matrix for a problem is as follows. Give the solutions to both the minimization problem and the dual maximization problem. Carefully label each solution. 1 -0.5 -0.7 0 0 15 1 -0.8
In Problems, complete both of the following.(a) State the given problem in a form from which the simplex matrix can be formed (that is, as a maximization problem with " constraints).(b) Form the
In Problems, the graph of the boundary equations for each system of inequalities is shown with that system. Locate the solution region and find the corners. – 3x + 4y < 18 -3x + 4y = 18 y 2х + y2
Use the simplex method to maximize f = 70x + 5y subject to x + 1.5y ≤ 150, x + 0.5y ≤ 90, x ≥ 0, and y ≥ 0.
In Problems, the graph of the boundary equations for each system of inequalities is shown with that system. Locate the solution region and find the corners. x + y < 25 4x + y< 40 3x + 8y 2 88 x 0, y
Use graphical methods to maximize f = 12x + 20y subject to3x + 5y ≤ 15009x + 5y ≤ 3600 x + 5y ≤ 1000x ≥ 0, y ≥ 0
In Problems, the graph of the boundary equations for each system of inequalities is shown with that system. Locate the solution region and find the corners. y x + 3y 2 6 2x + 4y 2 10 2x + 4y = 10 3x
Maximize f = 60x + 48y + 35z subject to 8х + бу + z < 108 4х + 2y + 1.5z < 50 2х + 1.5у + 0.5z 40 z< 16 x2 0, y 2 0, z20
In Problems, the graph of the boundary equations for each system of inequalities is shown with that system. Locate the solution region and find the corners. x + 4y 2 10 y 4x + 2y 2 10 x + y 2 4 x0, y
River Brewery is a microbrewery that produces an amber lager and an ale. Producing a barrel of lager requires 3 lb of corn and 2 lb of hops. Producing a barrel of ale requires 2 lb each of corn and
A marketing research group conducting a telephone survey must contact at least 150 wives and 120 husbands. It costs $3 to make a daytime call and (because of higher labor costs) $4 to make an evening
In Problems, use the simplex method to find the optimal solution. Assume that all variables are nonnegative.Minimize f = 2x + 3y subject to
In Problems, 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)
Lawn Rich, Inc., makes four different lawn care products that have fixed percents of phosphate, nitrogen, potash, and other minerals. The following table shows the percent of each of the four
In Problems, use the simplex method, Excel, or some other technology.A hospital wants to provide at least 24 units of nutrient A and 16 units of nutrient B in a meal while minimizing the cost of the
In Problems, use the simplex method to find the optimal solution. Assume that all variables are nonnegative.Minimize f = 3x + 9y subject to x ≤ 20
In Problems, 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)
In Problems, use the simplex method to find the optimal solution. Assume that all variables are nonnegative.Minimize f = 3x + 2y subject to
In Problems, 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)
In Problems, graph the solution of each system of inequalities. 3x + y> 1x - 2y < -1
In Problems, use the simplex method to find the optimal solution. Assume that all variables are nonnegative.Minimize f = 4x + y subject to
In Problems, 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)
In Problems, graph the solution of each system of inequalities. x + 5y < 200 < 134 2x + 3y < 134 x2 0, y 2 0
In Problems, use the simplex method to find the optimal solution. Assume that all variables are nonnegative.Maximize f = 2x + 5y subject to
In Problems, 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)
In Problems, graph the solution of each system of inequalities. —х + уS 2 X- х + 2у < 10 Зх + у 15 х> 0, у > 0
In Problems, use the simplex method to find the optimal solution. Assume that all variables are nonnegative.Maximize f = 3x + 2y subject to
In Problems, graph the solution of each system of inequalities. х+ 2y 48 х+ у 30 y
In Problems, graph the solution of each system of inequalities. Зх + у 9 Зх + 2у — 12 х+ 2y 8 x 0, y 2 0
In Problems, use the simplex method or Excel. Assume that all variables are nonnegative.Maximize f = 2x - y + 4z subject to
In Problems, graph the solution of each system of inequalities. х + 2у > 19 Зх + 2у > 29 х— 0, у 0
In Problems, use the simplex method or Excel. Assume that all variables are nonnegative.Maximize f = 5x + 2y + z subject to
Nekita Corporation assembles tablets and smartphones at two different factories in the same city. During each hour at the first factory, 150 tablets and 300 smartphones can be assembled at a cost of
In Problems, graph the solution of each system of inequalities. 4х + y > 12 х + у2 9 х + Зу 2 15 х— 0, у 2 0
In Problems, use the simplex method or Excel. Assume that all variables are nonnegative.Minimize f = 10x + 30y + 35z subject to
The Digital Star Company makes two different models of computer tablets, which are assembled on two different assembly lines. Line 1 can assemble 30 units of the Star model and 40 units of the
In Problems, graph the solution of each system of inequalities. х + Зу > 3 + 3у 2х + y2 3 2x x 0, y 2 0
In Problems, use the simplex method or Excel. Assume that all variables are nonnegative.Minimize f = x + 2y + z subject tox + 3y + 2z ≥ 40x + y + z ≥ 30x + y + z ≤ 100
In Problems, graph the solution of each system of inequalities. x + 2y 2 10 2x + y > 11 x + y2 9 x즈 0,y 0
In Problems, use the simplex method or Excel. Assume that all variables are nonnegative.Maximize f = 25x1 + 25x2 + 25x3 + 20x4 + 20x5 + 20x6 subject tox1 + x4 ≤ 100x2 + x5 ≤ 20x3 + x6 ≤
In Problems, graph the solution of each system of inequalities. х + 2у 20 — Зх + 2у 4 x + х2 12 x2 0, y 2 0
In Problems, use the simplex method or Excel. Assume that all variables are nonnegative.Minimize g = 480x1 + 460x2 + 440x3 + 420x4 + 530y1 + 510y2 + 490y3 + 470y4 - 9500 subject tox1 + y1 ≥
In Problems, graph the solution of each system of inequalities. Зх + 2y > 75 — Зх + 5у > 30 < 40 х> 0, у 2 0 y
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
The Digital Star Company makes two different models of computer tablets, which are assembled on two different assembly lines. Line 1 can assemble 30 units of the Star model and 40 units of the
Q-RAM Inc. manufactures solid-state drives (SSDs) of two sizes, 500 GB and 1.5 TB. The company can make a total of 60 drives per day, and it has available 120 labor-hours per day. It takes 1
In Problems, 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)
Two foods contain proteins, carbohydrates, and fats. Food A costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. Food B costs $1.50 per pound and contains 20% protein, 4% fat,
At one of its factories, a manufacturer of college logo sweatshirts makes two styles: crewneck pullover and hooded. Each pullover sweatshirt takes 5 minutes to cut out and 20 minutes to assemble and
At its Jacksonville factory, Nolmaur Electronics manufactures 4 models of TV sets: LCD models in 32-, 42-, and 50-in. sizes and a 65-in. plasma model. The manufacturing and testing hours required for
A bank has two types of branches. A satellite branch employs 3 people, requires $400,000 to construct and open, and generates an average daily revenue of $10,000. A full-service branch employs 6
Solve the equations in Problems. 2x + 5/x + 7 = 1/3 + x - 11/2x + 14
In Problem find the intercepts and graph the functions.5x – 6y = 30
In Problems, write the equation of each line described.Shown in the graph y 4 4 8 -4 00
In Problems, solve each system of equations. 6x + 3y = 1 у%3 — 2х + 1 ||
Solve 2x2 + 6x = 9.
Find the average rate of change ofP(x) = 92x – x2 – 1760over the interval from x = 10 to x = 40.
The wind chill expresses the combined effects of low temperatures and wind speeds as a single temperature reading. When the outside temperature is 0°F, the wind chill WC is a function of the wind
In Problems, perform the indicated matrix operations with the following matrices.AT + B 1 -2 -2 1 A = 3 B = 3 1 _4 1 1 4 -4 3 C = 2 - 1 D = 3 -1 5 41 2 3 3. 2.
In Problems, perform the indicated matrix operations with the following matrices.B - C 1 -2 -2 1 A = 3 B = 3 1 _4 1 1 4 -4 3 C = 2 - 1 D = 3 -1 5 41 2 3 3. 2.
In Problems, perform the indicated matrix operations with the following matrices.CD 1 -2 -2 1 A = 3 B = 3 1 _4 1 1 4 -4 3 C = 2 - 1 D = 3 -1 5 41 2 3 3. 2.
Ifdoes B = A-1? 1 2 1 1 A =| 0 3 and B = 1 1 0 1
In Problem multiply the matrices. [3 5 [1 6. 4,
In Problems, perform the indicated matrix operations with the following matrices.DA 1 -2 -2 1 A = 3 B = 3 1 _4 1 1 4 -4 3 C = 2 - 1 D = 3 -1 5 41 2 3 3. 2.
ifdoes C = D-1? -2 3 1 1 D = -3 and C 3. = -1 2 2. 3. 3.
Which of these matrices are square?Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
Find the inverse of the matrix 1 3 4, 2.
In Problem an augmented matrix for a system of linear equations in x, y, and z is given. Find the solution of each system. 1 1 2 -1 3 1 7 0 -2 4
In Problem an augmented matrix for a system of linear equations in x, y, and z is given. Find the solution of each system. 1 5 6. 0 -2 3 9. 1 3
What is the element a23?Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
Use the matrices below as needed to complete Problems.Perform the indicated operations in Problems3A - 5B 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 |
In Problems, find the inverse matrix for each matrix that has an inverse. 1 4 1 -1 2 1 1 3. 2.
For (a) Are F FT and FT F defined?(b) What size is each product?(c) Can F FT = FT F? Explain. 0 -1 3 F = -1 3 -4
In Problem use technology to solve each system of equations, if a solution exists. X1 + 2x2 X1 + 3x2 + 4x3 + X4 = 2x1 + 5x2 + 2x3 + 2x4 : X3 + X4 = 3 -2 1 %3D 2x1 + 3x2 6x3 + 2x4 3.
In Problems, perform the indicated matrix operations with the following matrices.BA 1 -2 -2 1 A = 3 B = 3 1 _4 1 1 4 -4 3 C = 2 - 1 D = 3 -1 5 41 2 3 3. 2.
In Problems, perform the indicated matrix operations with the following matrices.ABD 1 -2 -2 1 A = 3 B = 3 1 _4 1 1 4 -4 3 C = 2 - 1 D = 3 -1 5 41 2 3 3. 2.
Write the matrix that is the negative of matrix B.Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
Which industry is most dependent on the fuels industry?The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and
Find the inverse of the matrix 1 4 1 2 1 1 4

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