Linear Programming Questions and Answers

Use the simplex method to maximize the following:
Maximize f = 7x1 + 9x2 subject to
4x1 +5x2 ≤ 15
5x1 + 4x2 ≤ 32
4x1+5x2 ≤ 30
x1 ≥ 0, x2 ≥ 0
If no solutions exist enter DNE in all answerboxes.
x1 =
x2 =
f =
Math
Linear Programming
Use the simplex method to maximize the following: Maximize f = 7x1 + 9x2 subject to 4x1 +5x2 ≤ 15 5x1 + 4x2 ≤ 32 4x1+5x2 ≤ 30 x1 ≥ 0, x2 ≥ 0 If no solutions exist enter DNE in all answerboxes. x1 = x2 = f =
Use the objective function z = 10x + 12y to determine the maximum profit subject to the constraints
{x20 2x + 3y≤6 5x + 7y≤35 6x + 4y224 y21
Graph the feasible region, determine the corner points, and compute the maximum profit.
Math
Linear Programming
Use the objective function z = 10x + 12y to determine the maximum profit subject to the constraints {x20 2x + 3y≤6 5x + 7y≤35 6x + 4y224 y21 Graph the feasible region, determine the corner points, and compute the maximum profit.
Graph the solution of the system of linear inequalities.
ys-2x-2
y2x+4
Math
Linear Programming
Graph the solution of the system of linear inequalities. ys-2x-2 y2x+4
Graph the solution of the system of linear inequalities.
y + 2x20
3x-2y≤6
Math
Linear Programming
Graph the solution of the system of linear inequalities. y + 2x20 3x-2y≤6
Graph the solution of the system of linear inequalities.
y+4x20
4x-2y≤8
Math
Linear Programming
Graph the solution of the system of linear inequalities. y+4x20 4x-2y≤8
Alexia is reviewing for the Algebra End-of-Course exam. She made this graph representing a system of inequalities.
(6.2)
(5.4)
(2,-2)
(6,-3)
(2, 2)
(5, 1)
(2.-1)
(3.0)
Math
Linear Programming
Alexia is reviewing for the Algebra End-of-Course exam. She made this graph representing a system of inequalities. (6.2) (5.4) (2,-2) (6,-3) (2, 2) (5, 1) (2.-1) (3.0)
A high school band trip will require renting buses and trucks to transport no fewer than 150 students and 20 or more large instruments, Each bus can accommodate 60 students plus 3 large instruments; it costs $347 to rent. Each truck can accommodate 15 students plus 7 large instruments and costs $195 to rent. How many of each type of vehicle should be rented for the cost to be minimized?
Determine the minimum cost.
2 buses and 2 trucks: $1084
none of these
buses and 10 trucks: $1950
4 buses and 0 trucks: $1388
1 buses and 4 trucks: $1127
Math
Linear Programming
A high school band trip will require renting buses and trucks to transport no fewer than 150 students and 20 or more large instruments, Each bus can accommodate 60 students plus 3 large instruments; it costs $347 to rent. Each truck can accommodate 15 students plus 7 large instruments and costs $195 to rent. How many of each type of vehicle should be rented for the cost to be minimized? Determine the minimum cost. 2 buses and 2 trucks: $1084 none of these buses and 10 trucks: $1950 4 buses and 0 trucks: $1388 1 buses and 4 trucks: $1127
Two artists make winter yard ornaments. They get $97 for each wooden snowman
they make and $77 for each wooden Santa Claus. On average, Nina must work 4
hours and Roberta 3 hours to make a snowman. Nina must work 2 hours and Roberta 4 hours to make a Santa Claus. If neither wishes to work more than 20 hours per week, how many of each ornament should they make each week to maximize their income?

3 snowmen an 4 ornaments of Santa Claus: $19
4 snowmen an 3 ornaments of Santa Claus: $19
4 snowmen an 2 ornaments of Santa Claus: $542
5 snowmen an no ornaments of Santa Claus: $485
2 snowmen an 5 ornaments of Santa Claus: $23
Math
Linear Programming
Two artists make winter yard ornaments. They get $97 for each wooden snowman they make and $77 for each wooden Santa Claus. On average, Nina must work 4 hours and Roberta 3 hours to make a snowman. Nina must work 2 hours and Roberta 4 hours to make a Santa Claus. If neither wishes to work more than 20 hours per week, how many of each ornament should they make each week to maximize their income? 3 snowmen an 4 ornaments of Santa Claus: $19 4 snowmen an 3 ornaments of Santa Claus: $19 4 snowmen an 2 ornaments of Santa Claus: $542 5 snowmen an no ornaments of Santa Claus: $485 2 snowmen an 5 ornaments of Santa Claus: $23
Use the simplex method to maximize f= 4x + 4y + z under the constraints

x + 2y + 4z ≤ 20
2x + 4y + 4z ≤ 60
3x + 4y + z ≤ 90
x ≥ 0, y ≥ 0, z ≥ 0.
Math
Linear Programming
Use the simplex method to maximize f= 4x + 4y + z under the constraints x + 2y + 4z ≤ 20 2x + 4y + 4z ≤ 60 3x + 4y + z ≤ 90 x ≥ 0, y ≥ 0, z ≥ 0.
Two woodworkers, Tom and Carlos, earn a profit of $86 for making a table and $65
for making a chair. Tom must work 3 hours and Carlos 2 hours to make a chair. Tom
must work 2 hours and Carlos 6 hours to make a table. If neither wants to work more
than 42 hours per week, how many tables and chairs should they make to maximize
their profit?

3 tables and 12 chairs: $1038
13 tables and 2 chairs: $1227
notables and 15 chairs: $1806
12 tables and 3 chairs: $1227
none of these
Math
Linear Programming
Two woodworkers, Tom and Carlos, earn a profit of $86 for making a table and $65 for making a chair. Tom must work 3 hours and Carlos 2 hours to make a chair. Tom must work 2 hours and Carlos 6 hours to make a table. If neither wants to work more than 42 hours per week, how many tables and chairs should they make to maximize their profit? 3 tables and 12 chairs: $1038 13 tables and 2 chairs: $1227 notables and 15 chairs: $1806 12 tables and 3 chairs: $1227 none of these
Which of the following points lies in the solution region for y> 3 and y < -3.
(3,-3)
No solution
(0, 0)
Math
Linear Programming
Which of the following points lies in the solution region for y> 3 and y < -3. (3,-3) No solution (0, 0)
A company manufactures two models of snowboards, standard and deluxe. Each deluxe model requires 26 hours to produce, and 96 units of material. Each standard model requires 13 hours to produce and 80 units of material. The company has 858 production hours available and 4000 units of material in stock. The deluxe model sells for $272 and the standard model sells for $170. What amount of each model should be produced and sold to obtain the maximum revenue?
Adeluxe models
standard models
What is the maximum revenue? $
Math
Linear Programming
A company manufactures two models of snowboards, standard and deluxe. Each deluxe model requires 26 hours to produce, and 96 units of material. Each standard model requires 13 hours to produce and 80 units of material. The company has 858 production hours available and 4000 units of material in stock. The deluxe model sells for $272 and the standard model sells for $170. What amount of each model should be produced and sold to obtain the maximum revenue? Adeluxe models standard models What is the maximum revenue? $
Antonio wants to invest $7600 in a savings account that pays 7.9% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.
Math
Linear Programming
Antonio wants to invest $7600 in a savings account that pays 7.9% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.
The following data represents the amount of medication still in someone's system after specific amounts of time.
Time
(hours)   0        3         6         9        12       15
Meds
(mg)     500   255     129     66       33        15
What would a residual of -5 mean in context of this data?
a)The person actually had 5 mg more of medication in the blood than estimated.
b)The person actually had 5 mg of medication in the blood.
c)After 5 hours the person had their blood tested for medication.
d)The person actually had 5 mg less of medication in the blood than estimated.
Math - Others
Linear Programming
The following data represents the amount of medication still in someone's system after specific amounts of time. Time (hours) 0 3 6 9 12 15 Meds (mg) 500 255 129 66 33 15 What would a residual of -5 mean in context of this data? a)The person actually had 5 mg more of medication in the blood than estimated. b)The person actually had 5 mg of medication in the blood. c)After 5 hours the person had their blood tested for medication. d)The person actually had 5 mg less of medication in the blood than estimated.
Write an equation that models the linear situation:

The heater keeps the temperature of the pool at 78 degrees Fahrenheit all day long.

Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.

For example, DO NOT enter f(x) = 2x + 1

DO ENTER: f(x)=2x+1

Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use 33 for 1/3 because it is not exact, but you can use 0.25 for
1/4.)

To write your equation, use the variables:
h = amount of time since the day began (hours)
T(h) temperature of the pool (Fahrenheit degrees)
Equation:
Math
Linear Programming
Write an equation that models the linear situation: The heater keeps the temperature of the pool at 78 degrees Fahrenheit all day long. Instructions: DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1 Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2) You may use decimals IF the decimal values are exact. (You cannot use 33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.) To write your equation, use the variables: h = amount of time since the day began (hours) T(h) temperature of the pool (Fahrenheit degrees) Equation:
A local pizza shop has a membership program for frequent buyers. The membership costs $25 per month and members get a discounted price of $1.75 per slice of pizza. Isaac purchased a membership to this pizza shop. How much would Isaac have to pay the pizza shop if he bought 5 slices of pizza this month? What would be the monthly cost for a slices of pizza? 

Monthly cost with 5 slices: 
Monthly cost with a slices:
Math
Linear Programming
A local pizza shop has a membership program for frequent buyers. The membership costs $25 per month and members get a discounted price of $1.75 per slice of pizza. Isaac purchased a membership to this pizza shop. How much would Isaac have to pay the pizza shop if he bought 5 slices of pizza this month? What would be the monthly cost for a slices of pizza? Monthly cost with 5 slices: Monthly cost with a slices: