# Linear Programming Questions and Answers

Math

Linear ProgrammingA mail distribution center processes as many as 150,000 pieces of mail each day. The mail is sent via ground and air. Each land carrier takes 1800 pieces per load and each air carrier 1500 pieces per load. The loading equipment is able to handle as many as 150 loads per day. Let x be the number of loads by land carriers and y the number of loads by air carriers. Which system of inequalities represents this situation? Click on the correct answer.
1800x+1500y ≥150,000 x+y≥ 150
1500x+1800y ≥150,000 x+y≤ 150
1800x+1500y≤ 150,000 x+y≤150
1500x+1800y≤ 150,000 x+y≤150

Math

Linear ProgrammingSometimes linear systems are expressed in three variables. These can also be solved using linear combinations, but you need three equations to solve for all three variables. In this problem, there are three variables.
Ed decides to include more fruit in his diet. He goes to the grocery store over the weekend and buys 6 apples, 6 oranges, and 6 avocados. The total cost is $19.50.
Ed finishes the apples very quickly, and has some leftover avocado. The following weekend he buys 12 apples, 2 oranges, and 1 avocado. This time he pays just $9.50.
The following week, Ed reads an article on the benefits of avocado, so over the weekend he buys 5 avocados along with 2 apples and 4 oranges. His total this time is $14.
Assume that Ed pays a unit price rather than a price per pound for the apples, oranges, and avocados.

Math

Linear ProgrammingThe prices of a random sample of 24 new motorcycles have a sample standard deviation of $3626. Assume the sample is from a normally distributed population.
Construct a confidence interval for the population variance σ² and the population standard deviation 6. Use a 90% level of confidence. Interpret the results.
What is the confidence interval for the population variance σ²?
(Round to the nearest integer as needed.)

Math

Linear ProgrammingSolve the system analytically.
3x + 3y - 9z = 9
2x+y-z = 7
-x-y+ 3z=2
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. There is one solution. The solution set is
B. There are infinitely many solutions. The solution set is ,{(z)}, where z is any real number.
C. The solution set is Ø.

Math

Linear Programming1/ 100 people seated at different tables in a Mexican restaurant were asked if their party had ordered any of the following items: margaritas, chili con queso, or quesadillas
23 people had ordered none of these items.
11 people had ordered all three of these items.
29 people had ordered chili con queso or quesadillas but did not order margaritas.
41 people had ordered quesadillas.
46 people had ordered at least two of these items.
13 people had ordered margaritas and quesadillas but had not ordered chili con queso.
26 people had ordered margaritas and chili con queso.

Math

Linear ProgrammingSuppose a country has a population of 30 million and projects a growth rate of 3% per year for the next 20 years.
Find a formula for the population of the country after t years, where P is measured in millions of people.
P(t) =
What will the population of this country (in millions of people) be in 5 years? (Round your answer to two decimal places.)

Math

Linear ProgrammingA family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second
consumed 30 gallons of gas. The two cars drove a combined total of 2600 miles, and the sum of their fuel
efficiencies was 75 miles per gallon. What were the fuel efficiencies of each of the cars that week?

Math

Linear ProgrammingSuppose in one year, total revenues from digital sales of pop/rock, tropical (salsa/merengue/cumbia/bachata), and urban (reggaeton) Latin music in a certain country amounted to $21 million. Pop/rock music brought in twice as much as the other two categories combined and $11 million more than tropical music. How much revenue was earned from digital sales in each of the three categories?
pop/rock music $ million
tropical music $ million
urban Latin music $ million

Math

Linear ProgrammingThe sum of two numbers is 32. One number is 3 times as large as the other. What are the numbers?

Math

Linear Programming5
DR
Solve the linear programming problem using the simplex method.
Maximize z=2x, +5x₂ subject to
5Xq+xy 550
5x₁ + 2x₂ ≤70
X₁ + X₂ ≤60
X₁, X₂ ≥ 0.
*****
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The maximum is z =
when X₁ =
X2=S₁ = S₂ =
OB. There is no maximum solution for this linear programming problem.

Math

Linear ProgrammingSally likes to go buy groceries from Walmart or Shoprite
In Walmart, two pounds of tea and three pounds of coffee cost $19.00.
In Shoprite three boxes of milk and four cans of yoghurt cost $26.50.
Write the linear equations related to the details given, one equation for each stores.
Write an equation to represent the information given in the first
sentence.
define the variables you use
Equation:
Explain how you created the equation.
Hint: A linear equation is in standard form if it is in the form:
ar+by = c.

Math

Linear ProgrammingSystolic blood pressure is the higher number in a blood pressure reading. It is measured as the heart muscle contracts. Heather was with her grandfather when he had his blood pressure checked. The nurse told him that the upper limit of his systolic blood pressure is equal to half his age increased by 110.
a.a is the age in years, and p is the systolic blood pressure in millimeters of mercury (mmHg). Write an inequality to represent this situation.
b.Heather's grandfather is 76 years old. What is normal for his systolic blood pressure?

Math

Linear ProgrammingA 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 requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 1020 lb of beef, at most 600 lb of pork, and at least 500 lb of spices. If the profit is $1.85 on each pound of all-beef hot dogs and $1.00 on each pound of regular hot dogs, how many pounds of each should be produced to obtain maximum profit?
regular hot dogs 2000
all-beef hot dogs 880
What is the maximum profit? ✓lb lb

Math

Linear ProgrammingKelly works two jobs. She usually works at a retail store for 7 hours during the day and is paid $24.36 per hour by the store. In the evening she works at a restaurant as a manager for 7 hours and is paid $22.01 per hour. How much does she make on average per hour for the day?

Math

Linear ProgrammingThe test point (0, 0) is a representative point (Choose one) the line. Since (0, 0) satisfies the original inequality, then it and all other points (Choose one)
above
below
the line are solutions. Shade (Choose one) the line.

Math

Linear ProgrammingMia and her children went into a bakery where they sell cupcakes for $2.75 each and brownies for $1.25 each. Mia has $30 to spend and must buy at least 14 cupcakes and brownies altogether. If a represents the number of cupcakes purchased and y represents the number of brownies purchased, write and solve a system of inequalities graphically and determine one possible solution.

Math

Linear ProgrammingJosiah is taking his friends to the movies. Each ticket
costs $10, and popcorn is $5 a bag. There is a $3 service
fee for the entire purchase. He has $75. He buys 4 tickets,
and wants to figure out the maximum number of bags of
popcorn he can buy.
If x= number of tickets and y= number of bags of popcorn, which of the
following inequalities could you use to answer the problem?
A. 10x+ 5y≤ 75
B. 10x+ 5y+3 ≤75
C. 10x+ 5y + 3 ≥75
D. x+y= 75

Math

Linear ProgrammingThe area of a parking lot is 1710 square meters. A car requires 5 square meters and a bus requires 32 square meters of
space. There can be at most 180 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is $6.00, how
many buses should be in the lot to maximize income?
34
021
14
30

Math

Linear ProgrammingA carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width. Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.
A Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
B. The entire solution region is viable.
C. Part of the solution region includes a negative length; therefore, not all solutions are viable for the given situation.
D. No part of the solution region is viable because the length and width cannot be negative.

Math

Linear ProgrammingA nursery sells fertilizer in 25-pound and
100-pound bags. If Juliet bought 13 bags of ferti-
lizer for her landscaping business that contained
775 pounds of fertilizer, how many 100-pound bags
did she buy?
A) 5
B) 6
C) 7
D) 8