# Linear Programming Questions and Answers

Math

Linear ProgrammingA new car worth $21,000 is depreciating in value by $3000 per year. Complete parts (a) through (6).
a. Write a formula that models the car's value, y, in dollars, after x years,
b. Use the formula from part (a) to determine after how many years the car's value will be 39,000.
6. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then, show your solution to part (b) on the graph.
a. A formula that models the car's value, y, in dollars, after years is
(Type an equation.)

Math

Linear ProgrammingThere are 170 adults and 225 children at a zoo. The zoo makes a total of $4,740 from the entrance fees, and the cost of an adult and a child to attend is $24, how much does it cost each for a parent and a child?
Let a represent an adult.
Let c represent a child.
Enter a system of equations to represent the situation, then solve the system.

Math

Linear ProgrammingMeaghan goes to the grocery store to buy hot dogs and hamburgers for a cookout. She buys a total of 10 packages for a total of $37.40. If a package of hot dogs, d, costs $2.29 and a package of hamburgers, b, costs $5.19, determine how many packages of each she bought. Enter a system of equations to represent the situation, then solve the system.

Math

Linear ProgrammingA farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $5 per acre. Seed for crop B costs $10 per acre. The farmer can spend at most $550 on seed. If crop B brings in a profit of $60 per acre, and crop A brings in a profit of $90 per acre, how many acres of each crop should the farmer plant to maximize her profit?

Math

Linear ProgrammingA farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $10 per acre. Seed for crop B costs $20 per acre. The farmer can spend at most $500 on seed.
If crop B brings in a profit of $120 per acre, and crop A brings in a profit of $80 per acre, how many acres of each crop should the farmer plant to maximize her profit?

Math

Linear ProgrammingWhich of the following is the last step in solving a linear programming problem graphically?
Identify the corner points by solving systems of linear equations whose intersection represents a
corner point.
Test all corner points in the objective function.
Graph the constraints inequalities, and shade the feasible region
Write the objective function

Math

Linear ProgrammingAnthony's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y 57+ 6.3x, where y represents the expected quiz score and a represents hours spent on homework that week. What is the meaning of the x-value when y = 99?
A student's expected quiz score if they spent 1 hour on their homework. A student's expected quiz score if they spent 99 hours on their homework.
How many hours a student spends studying all year.
The number of hours a student should spend on their homework to expect a score of 99 on the quiz.

Math

Linear ProgrammingBob runs each lap in 7 minutes. He will run at most 12 laps today. What are the possible numbers of minutes he will run today?
Use for the number of minutes he will run today.
Write your answer as an inequality solved for t.

Math

Linear ProgrammingKevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 42 hours a week. He routinely completes at least 2 shocks replacements and 6 brake replacements a week. If he charges $500 for labor replacing shocks and $200 in labor for replacing brakes, how many jobs of each type should he complete a week to maximize his income?

Math

Linear ProgrammingA certain forest covers an area of 3500 km. Suppose that each year this area decreases by 6%. What will the area be after 5 years?

Math

Linear ProgrammingIn the lab, Dale has two solutions that contain alcohol and is mixing them with each other. He uses twice as much Solution A as Solution
B. Solution A is 17% alcohol and Solution B is 13% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has
376 milliliters of pure alcohol?
Number of milliliters of Solution B:[]
X
S ?

Math

Linear ProgrammingA company produces two types of TV stands. Type I has 6 drawers. It requires 3 single drawer pulls and 3 double drawer pulls. The company needs 75 hours of labor to produce the Type I TV stand. Type II has 3 drawers. It requires 6 single drawer pulls. The company needs 50 hours of labor to produce the Type II TV stand. The company only has 600 labor hours available each week, and a total of 60 single drawer pulls available in a week. For each Type I stand produced and sold, the company makes $200 in profit. For each Type II stand produced and sold, the company makes $150 in profit.
Part A
Identify the constraints as a system of linear inequalities. Let x represent the number of 6 drawer TV stands produced and let y represent the number of 3 drawer TV stands produced.

Math

Linear ProgrammingA calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators must be shipped each day. If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

Math

Linear ProgrammingA plumbing company charges a $125 just to come out and respond to an emergency call, and an additional $30 for every hour they are working. Find a formula for a linear model that will tell you how much total you need to pay them depending on how long they are working on the plumbing issue.

Math

Linear ProgrammingEaston is working two summer jobs, making $18 per hour tutoring and $9 per hour clearing tables. Last week Easton worked 4 times as many hours tutoring as he worked hours clearing tables hours and earned a total of $162. Graphically solve a system of equations in order to determine the number of hours Easton worked tutoring last week, x, and the number of hours Easton worked clearing tables last week, y.

Math

Linear ProgrammingA rental car company is running two specials. Customers can pay $20 to rent a compact car for the first day plus $14 for each additional day, or they can rent the same car for $50 the first day and $8 for every additional day beyond that. Harper notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How much would Harper pay in total? Write a system of equations, graph them, and type the solution.

Math

Linear ProgrammingFind the minimum and maximum values of z= 6x + 5y, if possible, for the following set of constraints.
5x + 4y ≥ 20
x+4y28
x20, y 20
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The minimum value is (Round to the nearest tenth as needed.)
B. There is no minimum value.

Math

Linear ProgrammingSandy worked 5.9 hrs on Monday, 6.8 hrs on Tuesday, and 8.2 hrs on Thursday. If she earns $11.25 per hour, how much money did she make that week? (round to the nearest cent) *
$2351.30
$23.51
$235.13
$235.12

Math

Linear ProgrammingSolve.
3≤2x+3≤ 13
Solve the inequality. Select the correct answer below, and if necessary fill in the answer box to complete your choice.
A. The solution set is
(Type a compound inequality.)
B. There is no solution.

Math

Linear ProgrammingAnna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.
y = 7.5x
y = 5.5x + 10
1. Substitute: 7.5x= 5.5x + 10
How many classes could Anna take so that the total cost for the month would be the same?
What is the total monthly cost when it is the same for both gyms?

Math

Linear ProgrammingA freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft and weighs 50 lb. The second product's unit volume is 3 cu ft, and it weighs 40 lb. If the company's trucks have 2,320 cu ft of space and can carry 21,100 lb, how many units of each product can be transported in a single shipment with one truck using the entire volume and weight capacity?
first product
second product

Math

Linear ProgrammingLola needs to rent a ballroom for a formal event. Ballroom S charges $52.50 per hour and one-time rental fee of $500. Ballroom T charges $62.50 per hour and a one-time rental fee of $300.
Which inequality can be used to find x, the minimum number of hours rented so that the total cost at Ballroom S is less than the total cost at Ballroom 7?
52.5r+ 500 > 62.5r + 300
52.5 +500x> 62.5 +300x
52.5 +500x < 62.5 +300x
52.5x + 500 < 62. 5x + 300

Math

Linear Programming4x - 5y = 7
3x - 4y = 6
a. Multiply the first equation by -3 and the second equation by 4.
b. Add the two equations, which eliminates x. Solve for y.
c. Substitute your value for y into the first equation. Solve for x.
Write the solution as an ordered pair.

Math

Linear ProgrammingYou are training for the upcoming bike and hike race. You plan on biking 8 miles each day and hiking 3 miles each day. By the end of the training you want to have covered at least 200 miles. Write a linear inequality to represent this situation. Let x represents distance
biked and y represent distance hiked.
8x + 3y > 200
8x + 3y ≤ 200
8x + 3y < 200
8x + 3y ≥ 200

Math

Linear ProgrammingYou lose your electronic tag that you use to pay tolls on the highway in your city. It costs you $24 to replace the tag. The cost of one toll when you don't use the tag is $3. The cost of the same toll when do use the tag is $1.50. How many times will you have to use the tag to pay for the tolls in order for the total cost to be the same as not
using the tag?

Math

Linear ProgrammingScenario: Deb works in an office in Miami and makes $42/hr. She must get her suit dry cleaned everyday for $75. If she wants to make more than $260 a day, at least how many hours must she work?

Math

Linear ProgrammingDeshaun takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Deshaun is taking a combined total of 12 credit hours at the two schools. Suppose that he is taking w credit hours at Westside. Write an expression for the combined total dollar amount he paid for his class fees.

Math

Linear ProgrammingSolve the system of equations by substitution.
2x-9y = 13
5x + 4y = 6
The solution of the system is x =
(Type integers or simplified fractions.)
and y=

Math

Linear ProgrammingDetermine if each ordered pair is a solution of the system of equations given.
3x + 5y = 19
x-3y = -3
a. (-3,2)
b. (3,2)
a. Is (-3,2) a solution to the linear system?

Math

Linear ProgrammingSolve the system by graphing.
y = 5x +4
y = 5x - 4
Use the graphing tool to graph the system.

Math

Linear ProgrammingSolve.
2 |5x-2|-3=4
Select the correct choice below and fill in any answer boxes within your choice.
A. The solution set is.
(Simplify your answer. Use a comma to separate answers as needed.)
B. The solution set is the empty set.

Math

Linear ProgrammingA delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 90 pounds. The truck is transporting
70 large boxes and 65 small boxes. If the truck is carrying a total of 6150 pounds in boxes, how much does each type of box weigh?
Note that the ALEKS graphing calculator can be used to make computations easier.

Math

Linear ProgrammingWhich of the following systems of inequalities would produce the region indicated on the graph below?
A v2 -x+4;y<x+2y20x20
B. V-x+4y>x+2y20x20
C. v≤-x+4y2x+2y20x20
D. V≤ -x+4;y<x+2y20x20

Math

Linear ProgrammingHow would you choose to reduce the system
shown to a 2 x 2? Explain why you would choose
this approach.
-3x + y - 2z = 10 (1)
5x - 2y - 2z = 12 (2)
x-y + z = 23 (3)

Math

Linear ProgrammingIf f(x) = 5x² + 6x, find each of the following.
(a) f(0) (b) f(-5) (c) f(3)
(a) f(0) = (Simplify your answer.)

Math

Linear Programmingslope of 4, point = (3, -5)
equation in point-slope form:
equation in slope-intercept form:

Math

Linear ProgrammingThe cost of a gym membership varies directly with the amount of months you have the membership. If a 3 month membership to the gym costs $215, and Jackson would like to be a member for 12 months. What is the total amount he will pay for 12 months?
A. $53.75
B. $29
C. $860
$500

Math

Linear ProgrammingGreta's Diner has a coffee club. If you join the club for a one-time fee of $12, it only costs $3 to buy a latte. If you choose not to join the club, it costs $4.50 to purchase a latte. At how many lattes will the two plans cost the same amount?

Math

Linear ProgrammingYaster Wood has two plants that produce lumber used in manufacturing tables and chairs. In 1 day of operation, plant A can produce the lumber required to manufacture 24 tables and 59 chairs, while plant B can produce the lumber required to manufacture 27 tables and 54 chairs. In this production run, the company needs enough lumber to manufacture at least 540 tables and 930 chairs.
It costs $935 per day to operate plant A and $980 per day to operate plant B. The company needs to produce sufficient lumber at a minimum cost. 0 This can be set up as a linear programming problem where you minimize the operational cost C. Introduce the decision variables:
x = number of days to use plant A
y = number of days to use plant B
Check all of the problem constraints. Note: The non-negative constraints are not included here.
27x + 24y ≥ 540
54x + 59y ≥ 930
24x + 59y ≥ 935
27x + 54y ≤ 980
59x + 54y ≥ 930
24x + 27y ≥ 540

Math

Linear ProgrammingInvestor Matt has $83,000 to invest in a CD and a mutual fund. The CD yields
4% and the mutual fund yields an average of 8.5%. The mutual fund requires a
minimum investment of $10,000, and Matt requires that at least 2 times as
much money be invested in the CD as in the mutual fund. You must invest in
these bonds to maximize his return.
This can be set up as a linear programming problem. Introduce the decision
variables:
x = dollars invested in the CD
y = dollars invested in the mutual fund
Check all of the problem constraints. Note: The non-negative constraints are
not included here.
0.04x + 0.085y ≤ 83000
x+y2 10000
y≥ 2x
y ≤ 10000
0.04x+0.085y ≥ 10000
y ≥ 10000
AUD
x + y ≤ 83000
x ≥ 2y
x ≥ 10000

Math

Linear ProgrammingJesaki Furniture Company has two plants that produce lumber used in
manufacturing tables and chairs. In 1 day of operation, plant A can produce the
lumber required to manufacture 22 tables and 61 chairs, while plant B can
produce the lumber required to manufacture 28 tables and 51 chairs. In this
production run, the company needs enough lumber to manufacture at least 440
tables and 830 chairs.
It costs $875 per day to operate plant A and $850 per day to operate plant B.
The company needs to produce sufficient lumber at a minimum cost.
This can be set up as a linear programming problem where you minimize the
operational cost C. Introduce the decision variables:
x = number of days to use plant A
y = number of days to use plant B
Find the objective function C.
C = 61x + 5ly
C = 22x + 28y
C= 875x + 850y
C = 440x + 830y
C = 850x + 875y

Math

Linear ProgrammingA company has $10,290 available per month for advertising. Newspaper
ads cost $140 each and can't run more than 20 times per month. Radio
ads cost $370 each and can't run more than 31 times per month at this
price.
Each newspaper ad reaches 6650 potential customers, and each radio
ad reaches 7900 potential customers. The company wants to maximize
the number of ad exposures to potential customers.
Use n for number of Newspaper advertisements and r for number of
Radio advertisements.
Maximize P =
< 20
<31
<$10, 290
subject to
Enter the solution below. If needed, round ads to 1 decimal palace and
group exposure to the nearest whole person.
Number of Newspaper ads to run is
Number of Radio ads to run is
Maximum target group exposure is
people

Math

Linear ProgrammingDavid runs a factory that makes Blu-ray players. Each R80 takes 8 ounces of plastic and 3 ounces of metal. Each D200 requires 4 ounces of plastic and 6 ounces of metal. The factory has 368 ounces of plastic, 444 ounces of metal available, with a maximum of 20 R80 that can be built each week. If each R80 generates $17 in profit, and each D200 generates $14, how many of each of the Blu-ray players should David have the factory make each week to make the most profit?

Math

Linear ProgrammingZoey has a total of 16 coins. Some of her coins are dimes and some are nickels. The combined value of her dimes and nickels is $1.35. How many dimes and nickels does she have?
Step 1: Identify the variables.
Step 2: Set up the system.
Step 3: Solve the system.
Step 4: Answer the question.

Math

Linear Programming- For each boat he sells, Mick earns $149 in addition to 2% of the purchase price of the boat as
commission. If p represents the purchase price of the boat, which equation represents Mick's
commission, c?
A.
B.
C.
D.
c=149+.2p
c=149+.02p
p=149+.2c
p=149+.02c

Math

Linear ProgrammingA computer backs up 324 megabytes of data in 5 minutes.
Write an equation that represents the number of megabytes, m, that can be backed up in t minutes.
m=
64.8
t
Write an equation that can be used to approximate the number of minutes, t, required to back up m
megabytes of data. Round this answer to the nearest thousandth.
t=
m

Math

Linear ProgrammingWolfrich lived in Portugal and Brazil for a total period of 14 months in order to learn Portuguese.
He learned an average of 130 new words per month when he lived in Portugal and an average of 150 new
words per month when he lived in Brazil. In total, he learned 1920 new words.
How long did Wolfrich live in Portugal, and how long did he live in Brazil?
Wolfrich lived in Portugal for
Show Calculator
months and lived in Brazil for
months.

Math

Linear ProgrammingSandy is upgrading her Internet service. Fast Internet charges $30 for installation and $46.45 per month. Quick Internet has free installation but charges $53.95 per month.
Complete the equation that can be used to find the number of months after which the Internet service would cost the same. Use the variable x to represent the number of months of Internet service purchased.
The equation is__+0

Math

Linear ProgrammingComplete the description of a real-world situation that could be modeled by the equation 20 +1.25x = 15 +2.5x. plus $1.25 per hour to keep a dog A pet sitter charges a flat fee of $ during the day. A second pet sitter charges a flat fee of $15 plus $ hour. After (select) per is the charge for the two pet sitters the same?

Math

Linear ProgrammingA punch recipe requires 3 1/4 cups of orange juice. The recipe makes 4 quarts of punch. If you were to make
10 quarts of punch, how many cups of orange juice would you need?
08 1/1/0
07/1/20
083/0
06
78