# Linear Programming Questions and Answers

Math

Linear ProgrammingGraph this inequality:
y < 3
Plot points on the boundary line. Select the line to switch between solid and dotted. Select a
region to shade it.

Math

Linear ProgrammingThe cost per ounce of a drink, c, in cents, varies inversely as the number of ounces, n. Six ounces of the drink costs 60 cents per ounce. Find the equation that represents this relationship.

Math

Linear ProgrammingA car dealership wants to try out a new leasing arrangement, which will allow a buyer to trade a car back to the dealership for a certain amount of credit at any time throughout the first four years of ownership. For a car in good condition, the arrangement will value the car at 1/4 the original price at the end of four years, and will depreciate the value of the car linearly over the course of the four years. What is the value of a car with initial purchase price Pat the end of the first year? Write your answer as an expression in terms of P. Write the exact answer. Do not round.

Math

Linear ProgrammingAbigail has $400 in her savings account. She wants to keep at least $160 in the account. She withdraws $40 each week for food. Write and solve an inequality to show how many weeks she can make withdrawals from her account.

Math

Linear ProgrammingA dumpster in the shape of a rectangular prism has a volume of 528 cubic feet. The length of the dumpster is 5 feet less
than twice the width w, and the height is 2 foot less than the width.
Find the equation, in terms of w, that could be used to find the dimensions of the dumpster in feet. Your answer should be
in the form of a polynomial equals a constant.

Math

Linear ProgrammingA shop has one-pound bags of peanuts for $2.00 and three-pound bags of peanuts for $5.50. If you buy 5 bags and spend $17.00, how many of each size bag did you buy?
4 one-pound bags; 1 three-pound bag
2 one-pound bags; 3 three-pound bags
1 one-pound bag; 4 three-pound bags
3 one-pound bags; 2 three-pound bags

Math

Linear ProgrammingThe sum of two numbers is 56. The difference of the two numbers is 32. What are the two numbers.
Let a be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 56."
Write an equation that expresses the information in the sentence "The difference of the two numbers is 32."

Math

Linear ProgrammingThe number of women elected to the U.S. House of Representatives has increased nearly every Congress since 1985. In the 99th Congress, beginning in 1985, there were 22 female representatives. In the 109th Congress, beginning in 2005, there were 68 female representatives. Write a linear equation that models the number of female members of the House of Representatives x years after 1985.

Math

Linear ProgrammingLeah and Christopher work at a dry cleaners ironing shirts. Leah can iron 25 shirts per hour, and Christopher can iron 15 shirts per hour. Leah and Christopher worked a combined 13 hours and ironed 265 shirts. Write a system of equations that could be used to determine the number of hours Leah worked and the number of hours Christopher worked. Define the variables that you use to write the system.

Math

Linear ProgrammingKolby decided he wanted to go to the amusement park. The amusement park charges
$8.00 for entry and $1.40 for each ride.
Part A
Write an expression to represent this scenario where r represents the number of
rides.
Part B.
Write and solve an equation to determine how many rides Kolby can ride if his parents gave him $26.00. Show your work.

Math

Linear ProgrammingFrank plans to spend no more than $85 on plants for his front garden. He purchases
salvia and three azaleas. The azaleas cost $22 each.
Let c be the cost for a salvia. Which inequality below could be used to show how
3c+22≥ 85
3 x 22 + c ≥85
3c+22≤85
3 × 22 + c ≤ 85

Math

Linear ProgrammingSuppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function:
I(x) = 1054x + 23,286
where is the number of years after 1990.
Which of the following interprets the slope in the context of the problem?
Select the correct answer below:
In 1990, average annual income was $1,054.
In the ten-year period from 1990 to 1999, average annual income increased by a total of $23,286.
O Each year in the decade of the 1990s, average annual income increased by $1,054.
O Average annual income rose to a level of $23,286 by the end of 1999.

Math

Linear ProgrammingA day-care center invests $25,000 to set up a new facility. The center plans to charge $550 per student per year. Write a
linear model in the form y = mx + b where y represents the amount of profit the center earns for enrolling a number of
students.
Provide your answer below:

Math

Linear ProgrammingYou take a package to the local shipping company. They charge a fixed base cost of $6 per package plus an additional $0.39 per pound. If P represents the number of pounds of your package, and C is the total cost of shipping your package, write the linear equation that represents the relationship between P and C. Provide your answer below:

Math

Linear ProgrammingFind a linear equation to model this real-world application:
It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The
company has monthly operating expenses of $350 for utilities and $3300 for salaries. Write the linear equation to model
the company's monthly expenses in the form of y
mx + b.
=
Do not include commas in your answer.
Provide your answer below:

Math

Linear ProgrammingWatch the video that describes solving a quadratic inequality.
Click here to watch the video.
Solve the inequality analytically. Support your answer graphically.
9x²-30x>-25
The solution set is
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Math

Linear ProgrammingA caterer offers a package that feeds up to 50 people for $1,500 and adds an additional charge of $24.75 for each additional person. Enter a linear model that represents the total amount charged a host, t, as a function of g, the number of additional guests.

Math

Linear ProgrammingA manufacturer wishes to make tee-shirts for the band Dixie Chicks. They sell for $15 each.
She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some
machines. Once all machines are set up she will turn them on. Each machine takes one day
to set up. A machine produces 200 shirts in one day. All the machines must be set up before
any of them are turned on. Express the total amount of money M she will receive for the
shirts in terms of the number n of machines she decides to set up (assuming she sells all the
shirts she makes).
M(n) = $

Math

Linear ProgrammingWrite an equation that models the linear situation:
12 gallons are drained from a pool every minute. The pool began with 15,000 gallons in it.
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:
t = amount of time pool has been draining (minutes)
W(t)= amount of water drained from the pool (gallons)

Math

Linear ProgrammingNov 05, 4:2
Mariana signed up for a streaming music service that costs $7 per month. The service
allows Mariana to listen to unlimited music, but if she wants to download songs for
offline listening, the service charges $1.25 per song. How much total money
Mariana have to pay in a month in which she downloaded 40 songs? How much
would she have to pay if she downloaded s songs?
would

Math

Linear ProgrammingWrite an equation that models the linear situation:
A train starts a trip of 420 miles and it travels at a steady (average) speed of 70 miles per hour.
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:
t = time traveled (hours)
d(t) = distance left to travel (miles)
Equation:

Math

Linear ProgrammingSolve the system using Gaussian elimination or Gauss-Jordan elimination.
8x+10y = -17
4x + 5y = -9
Select one:
a. {}
b. ((-5x/4-9/4,2y) ly is any real number}
c. {(-17, -9)}
d. {(-7, 7)}

Math

Linear ProgrammingA red candle is 8 inches tall and burns at a rate of 7/10 inch per hour.
A blue candle is 6 inches tall and burns at a rate of 1/5 inch per hour.
After how many hours will both candles be the same height? Enter your answer in the box.

Math

Linear ProgrammingAn objective function and a system of linear inequalities representing constraints
are given. Complete parts a. through c.
Objective Function z = 3x+y
Constraints
x≥0, y ≥ 0
4x + 3y ≤ 24
x+y≥4
a. Graph the system of inequalities representing the constraints.
Use the graphing tool to graph the system.

Math

Linear ProgrammingDuring the month of August, the mean of the daily rainfall in one city was 0.04 inches
with a standard deviation of 0.15 inches. In another city, the mean of the daily rainfall
was 0.01 inches with a standard deviation of 0.05 inches.
Han says that both cities had a similar pattern of precipitation in the month of
August. Do you agree with Han? Explain your reasoning

Math

Linear ProgrammingSolve Linear System Graphically (Lev. 1)
Solve the following system of equations graphically on the set of axes
below.
y=3x-6
y=-x+2

Math

Linear ProgrammingUse the equation of the line of best fit, y=0.93x+8.07, to answer the questions below.
Give exact answers, not rounded approximations.
(a) For an increase of one year of experience, what is the
predicted increase in the hourly pay rate?
(b) What is the predicted hourly pay rate for a cashier who
doesn't have any experience?
(c) What is the predicted hourly pay rate for a cashier with
5 years of experience?

Math

Linear ProgrammingCasey bought a 15.4-pound turkey and an 11.6-pound ham for Thanksgiving and paid $38.51. Her friend Jane bought a 10.2-pound turkey and a 7.3-pound ham from the same store and paid$24.84. Find the cost per pound of turkey and the cost per pound of ham.

Math

Linear ProgrammingA recipe for soup calls for 4 tablespoons of lemon juice and 2
50.
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the chef need for the larger batch?
a) The chef needed
(Type a whole number,
cup of olive oil. The given recipe serves 5 people, but a cook wants to make a larger batch that serves
cups of lemon juice for the larger batch.
proper fraction, or a mixed number.)
b) The chef needed
pints of olive oil for the larger batch.
(Type a whole number, proper fraction, or a mixed number.)

Math

Linear ProgrammingKaj and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $4.75 and a drink for $3.75. How much would it cost if they bought 6
bags of popcorn and 3 drinks? How much would it cost if they bought p bags of
popcorn and d drinks?
Total cost, 6 bags of popcorn and 3 drinks:
Total cost, p bags of popcorn and d drinks:

Math

Linear ProgrammingA commercial aircraft gets the best fuel efficiency if it operates at a minimum altitude of 29,000 feet and a maximum altitude of 41,000 feet. Model the most fuel- efficient altitudes using a compound inequality.
x 29,000 and x ≤ 41,000
xs 29,000 and x ≥ 41,000
x≥ 41,000 and x ≥ 29,000
xs 41,000 and x =29,000

Math

Linear ProgrammingJoseph accepted a new job at a company with a contract guaranteeing annual raises. Joseph will get a raise of $5000 every year and had a starting salary of $70000. Write an equation for S, in terms of n, representing Joseph's salary after working n years for the company.

Math

Linear ProgrammingJosi has a job in which she works 30 hr/wk and gets paid $5/hr. If she works more than 30 hr in a
week, she receives $8/hr for each hour over 30 hr. If she worked 38 hr this week, how much did
she earn?

Math

Linear ProgrammingDetermine the number of slack variables and name them. Then use the slack
variables to convert each constraint into a linear equation.
How many and which slack variables should be assigned?
st)
cias
A. There are three slack variables named x_1, x_2, s_1
B. There are five slack variables named x_1, x 2, s_1, s_2, s_3.
c. There are three slack variables named s_1, s_2, s_3.
D. There are two slack variables named s_1, s_21
Assume the first equation using a slack variable is 5x₁ - x_2+s₁ = 164. What is
the second equation after the slack variable is introduced?
OA. 15x₁ +6x2 +5₁ +5₂ =201
OB. 15x, +6x₂ +S₁ =201
OC. 15x₁ +6x2 +52 = 201
Maximize z= 8x₁ + 3x_2
subject to:
with
5X, -X_2's 164
15x₁ + 6x 2 s 201
10x 1 + x 2
X₁20
≤ 340
x 220

Math

Linear ProgrammingA diet is to contain at least 1480 units of carbohydrates, 2140 units of proteins, and 1960 calories. Two foods are available: F which costs $ 0.09 per unit and F2, which costs $ 0.05 per unit.
A unit of food F₁ contains 2 units of carbohydrates, 4 units of proteins and 6 calories. A unit of food F2 contains 8 units of carbohydrates. 6 units of proteins and 4 calories.
Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutrition requirements.
Corner points of the feasible region:
If there is more than one corner point, type the points separated by a comma (i.e. (1,2).(3,4)).

Math

Linear ProgrammingSo, the predicted hourly pay rate is $8.19.
Note that this value is equal to the y-intercept of the line of best fit.
(b) For an increase of one year in experience, we want the predicted increase in the hourly pay rate.
The slope of the line of best fit is 0.91.
So for an increase of one year in experience, x, the predicted increase in the hourly pay rate, y, is $0.91.
(c) We want the predicted hourly pay rate for a cashier with 5 years of experience.
To get this, we let x = 5 in the equation y=0.91x+8.19.
y=0.91(5)+8.19 = $12.74
So, the predicted hourly pay rate is $12.74.

Math

Linear ProgrammingA local water park found that if the price of admission was $18, the attendance was about 2300 customers per week. When the price of admission was dropped to 99,
attendance increased to about 2500 per week. Write a linear equation for the attendance in terms of the price,p. (A mp + b)

Math

Linear ProgrammingA chain saw requires 8 hours of assembly and a wood chipper 4 hours. A maximum of 64 hours of assembly time is available. The profit is $170 on a chain saw and
$230 on a chipper How many of each should be assembled for maximum profit?
To attain the maximum profit, assemble
chain saws and
wood chippers

Math

Linear ProgrammingA chain saw requires 6 hours of assembly and a wood chipper 8 hours. A maximum of 144 hours of assembly time is available. The profit is $160 on a chain saw and
$210 on a chipper. How many of each should be assembled for maximum profit?
To attain the maximum profit, assemble
chain saws and
wood chippers

Math

Linear ProgrammingSESMUM & bas
3. The difference between two numbers is 32. The second number is
1 less than 5 times the first number. What are the numbers?id end

Math

Linear ProgrammingA movie theater charges $15 for standard viewing, $20 for 3D viewing, and $35 for Dinner and a Movie viewing. There are four times as many 3D viewing seats as Dinner and a Movie seats. If the theater brings in $53,000 when tickets to all 3000 seats are sold, determine the quantity of each type of seat in the movie theater.

Math

Linear ProgrammingFind the minimum and maximum values of z=2x +9y, if possible, for the following set of constraints
x+y≤5
-x+y≤1
2x-y≤6
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
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The maximum value is (Round to the nearest tenth as needed.)
B. There is no maximum value

Math

Linear ProgrammingLiz is working to raise money for breast cancer research. She discovered that each church group requires 2 hours of letter writing and 1 hour of follow-up, while each neighborhood group needs 2 hours of letter writing and 3 hours of follow-up. Liz can raise $150 from each church group and $200 from each neighborhood group, and she has a maximum of 12 hours of letter-writing time and a maximum of 16 hours of follow-up time available per month. Use the simplex method to complete parts (a) and (b).
(a) Determine the most profitable mixture of groups Liz should contact and the most money she can raise in a month.
Set up the linear programming problem. Let x, and x2 represent the numbers of church groups and neighborhood groups, respectively, and let z be the total amount of money raised.
(Do not factor. Do not include the $ symbol in your answers.)

Math

Linear ProgrammingCoretta studies falcons. In one region, she finds 94 females and 47 males. Coretta claims this is
always the proportion of females to males among falcons. In another region, there are 84 falcons.
How many of the 84 falcons must be females to support Coretta's claim?

Math

Linear ProgrammingBrittany brought her collection of Map Mosaics jigsaw puzzles to a secondhand store to sell. She was paid cash for all 8 puzzles in her collection. Before she left, Brittany used $7.25 of her earnings to purchase a used board game. She had $12.75 remaining. Which equation can you use to find the amount of money, p, Brittany received for each puzzle in her collection?

Math

Linear ProgrammingUB faculty union is organizing a trip for at least 600 of its members to visit the new water park at Bahamar. Bahamar has indicated there are only 14 tour guides available and tours can be done in groups of 50 at $800 or groups of 40 at $600. Calculate the number of tours needed at $600 to minimize the cost of the trip.

Math

Linear ProgrammingA truck can be rented from Company A for $80 a day plus $0.40 per mile. Company B charges $20 a day plus $0.70 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

Math

Linear ProgrammingThe drama department is selling adult tickets, x, for $10 per ticket and student tickets, y, for $7 per ticket. They want to make at least $2000 on ticket sales. The auditorium has 300 seats. Write a system of inequalities to model the situation, graph using Desmos, and give a possible solution.
A possible solution is ... adult tickets and ... student tickets.

Math

Linear ProgrammingDoreen Schmidt is a chemist. She needs to prepare 32 ounces of a 12% hydrochloric acid solution. Find the amount of 16% solution and the amount of 8% solution she should mix to get this solution.
How many ounces of the 16% acid solution should be in the mixture?
How many ounces of the 8% acid solution should be in the mixture?