A refinery produces two grades of gasoline, regular and premium, by blending together three components, A, B, and C. Component A has an octane rating of 90 and costs $24 a barrel, component B has an octane rating of 100 and costs $34 a barrel, and component C has an octane rating of 110 and costs $36 a barrel. The octane rating for regular must be at least 95 and the octane rating for premium must be at least 105. Regular gasoline sells for $40 a barrel and premium sells for $46 a barrel. The company has 45,000 barrels of component A, 30,000 barrels of component B, and 15,000 barrels of component C, and must produce at least 35,000 barrels of regular and 25,000 barrels of premium. How should the components be blended in order to maximize profit?

A refinery produces two grades of gasoline, regular and premium, by blending together three components, A, B, and C. Component A has an octane rating of 90 and costs $24 a barrel, component B has an octane rating of 100 and costs $34 a barrel, and component C has an octane rating of 110 and costs $36 a barrel. The octane rating for regular must be at least 95 and the octane rating for premium must be at least 105. Regular gasoline sells for $40 a barrel and premium sells for $46 a barrel. The company has 45,000 barrels of component A, 30,000 barrels of component B, and 15,000 barrels of component C, and must produce at least 35,000 barrels of regular and 25,000 barrels of premium. How should the components be blended in order to maximize profit?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: A roasting company makes a homemade blend of coffee 8 from two kinds of beans: Java beans, at $14.89…

A: topic - percentage

Q: Two types of carbonated drinks are to be mixed. One of them contains 1% sugar, and the other…

Q: The number of patrol officers needed on staff depends on the crime rate of the county, which is…

Q: A diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Researchers are investigating the effectiveness of using a fungus to control the spread of an insect…

A: (a) The treatments, experimental units and response variables are as follows : Treatments : 4…

Q: A chemist has two alloys of bronze, one that is 12% tin and 88% copper, and a second that is 10% tin…

A: Given, 12% tin and 88% copper in alloy 1. 10% tin and 90% copper in alloy 2. Consider 100 g quantity…

Q: The number of patrol officers needed on staff depends on the crime rate of the county, which is…

Q: Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has…

A: Let the quantity of Toot of noisemaker be x1, quantity of Wheet of noisemaker be x2 and quantity of…

Q: The number of patrol officers needed on staff depends on the crime rate of the county, which is…

A: The objective of the question is to calculate the number of police officers needed in Maple County…

Q: You recently received a job with a company that manufactures an automobile anti theft device. To…

A: State the hypotheses. That is, there is no evidence to conclude that the standard deviation of the…

Q: A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has…

A: Let us solve the given LPP problem with the help of Simplex method in the next steps.

Q: As a feed salesman you are responsible to prepare a 27 percent crude protein mixture that consists…

A: Given crude protein amount in corn meal as 13% Given crude protein amount in soybean meal as 45% To…

Q: For every pound of flour a baker adds 2.2 oz. of additives. If there is 15% of additive A, 25% of…

A: Given : For every pound of flour a baker adds 2.2 oz. of additives. there is 15% of additive A, 25%…

Q: Researchers are investigating the effectiveness of using a fungus to control the spread of an insect…

A: The treatments, experimental units and response variables are as follows :

Q: Select the correct answer. A veterinarlan is mixing three different types of feed to produce a…

Q: Because of new federal regulations on pollution, a chemical plant introduced a new, more expensive…

A: let the gallon produced by older process =x let the gallon produced by new process =y according to…

Q: Researchers are investigating the effectiveness of using a fungus to control the spread of an insect…

A: (c) Treatments have to be randomly assigned to experimental units so that each treatment has same…

Q: If their van averages 25 mpg, estimate how many gallons of gasoline are needed for the trip. Select…

Q: A computer manufacturer buys 30% of its chips from supplier A and the rest from supplier B. Two…

A: It is given that, 30% of computer chips are brought from supplier A, and rest from supplier B, while…

Q: Consider a person who invests in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average…

Question

A refinery produces two grades of gasoline, regular and premium, by blending together three components, A, B, and C. Component A has an octane rating of 90 and
costs $24 a barrel, component B has an octane rating of 100 and costs $34 a barrel, and component C has an octane rating of 110 and costs $36 a barrel. The octane
rating for regular must be at least 95 and the octane rating for premium must be at least 105. Regular gasoline sells for $40 a barrel and premium sells for $46 a
barrel. The company has 45,000 barrels of component A, 30,000 barrels of component B, and 15,000 barrels of component C, and must produce at least 35,000
barrels of regular and 25,000 barrels of premium. How should the components be blended in order to maximize profit?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

An allergy pill contains 180 mg of medicine. 10% of the medicine is eliminated from the patient's body every hour. To be effective, 70 mg of the medicine needs to be in the patient's body. If the patient takes one pill at 8 am, should they still be allergy-free at 5 pm?
As a feed salesman you are responsible to prepare a 27 percent crude protein mixture that consists of corn meal (13% CP) and soybean meal (45% CP). If you make 100 lbs of the ration what is the % CP for soybean meal for the ration and what is the percent corn meal needed for the ration?
Mr. and Mrs. Wagner are getting ready to drive across the US from Philadelphia, PA to Los Angeles, CA over five (5) days. The TOTAL distance is approximately 3,000 miles. The average price of gasoline is $4.10 per gallon. They plan to stay in a hotel four (4) nights. They are budgeting $50 per day per person to cover the cost of three (3) meals per day each. If their van averages 25 mpg, estimate how many gallons of gasoline are needed for the trip. Select the correct answer below.
A roasting company makes a homemade blend of coffee 8 from two kinds of beans: Java beans, at $14.89 per kilogram, and Sumatra beans, 6 $12.25 per kilogram. The roaster prepares 50 kg of house blend and the cost of the beans is $13.99 per kilogram. On the bags of house blend coffee, the roaster must indicate the percentage of each kind of beans that he used.Calculate the percentage of each blend.
A computer manufacturer buys 30% of its chips from supplier A and the rest from supplier B. Two percent of the chips from supplier A are defective, as are 4% of the chips from supplier B. Approximately what percentage of the defective chips are from supplier B?
A chemist has two alloys of bronze, one that is 12% tin and 88% copper, and a second that is 10% tin and 90% copper. If these two alloys are melted and thoroughly mixed together, between what two values is the percent of tin in the mixture? 18.
The number of patrol officers needed on staff depends on the crime rate of the county, which is calculated based on the number of crimes per year. At a 3% crime rate, the county hires 200 officers per 10,000 people in the population. For every 0.1% increase in crime rate, an additional 5 officers are hired per 10,000 people in the population. For every 0.1% below 3% crime rate, 3 fewer officers are hired. • A 3% sign-on bonus is offered for officers with no experience when there is a 5% to 10% shortage in the number of officers employed. • A 5% sign-on bonus is offered for officers with no experience when there is an 11% or higher shortage in the number of officers employed. • A 6% sign-on bonus is offered for officers with at least 3 years of experience when there is a 5% to 10% shortage in the number of officers employed. • A 10% sign-on bonus is offered for officers with at least 3 years of experience when there is an 11% or higher shortage in the number of officers employed. County…
A steakhouse forecasts 150 customers and typically 18% of the guests order the chicken. The yield is 73% and each portion is 6oz. The chef has 3# in the inventory, how many pounds of chicken should the chef order and round up the nearest pound as a safety net. Select one: a. 12# b. 11# с. 10# d. 14#
Consider a person who invests in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 6.5% on AAA bonds, 7% on A bonds, and 9% on B bonds. The person invests twice as much in B bonds as in A bonds. Let x, y and z represent the amounts invested in AAA, A, and B bonds, respectively. x + y + z = 10,000(total investment) 0.065x + 0.07y + 0.09z = 760(annual return) 2y – z = 0 Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond. Total Investment Annual Return $10,000 760
A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has two feathers, and is sprinkled with 0.5 oz of sequin powder. A Honk requires 30 minutes, has three feathers, and one oz. of sequin powder. The net profit is $0.40 per Toot, $0.50 per Wheet, and $0.80 per Honk. The following resources are available: 80 hrs of labor, 360 feathers, and 90 oz. of sequin powder. Determine the quantity of each type of noisemaker that maximizes profit.
A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has two feathers, and is sprinkled with 0.5 oz of sequin powder. A Honk requires 30 minutes, has three feathers, and one oz. of sequin powder. The net profit is $0.40 per Toot, $0.50 per Wheet, and $0.80 per Honk. The following resources are available: 4800 minutes of labor, 360 feathers, and 90 oz. of sequin powder. Determine the quantity of each type of noisemaker that maximizes profit.
An engineer was interested in the effect of two factors on strength of sheet castings of a polymer. One factor was time in a polymerization bath with 1% catalyst. The other factor was the temperature of the polymerization bath. The engineer tried two times (20 minutes and 60 minutes) and two temperatures (100 and 120 degrees F). He treated samples of polymer under each of the four sets of conditions. Then he measured flexural strength (in pounds per square inch, or psi) on samples of sheet castings of the polymer. The results are shown in the table below: 100 degrees 20 minutes 9500 10650 9700 9950 10100 60 minutes 11500 11650 11250 11250 11900 120 degrees 11300 11750 11600 11650 11700 10900 11500 11850 11700 11650 Test for main factor effects or factor interactions, at the 5% significance level.