Homework Help is Here – Start Your Trial Now!
Math
Probability
contains 90 IU of vitamin A, 3 mg of vitamin B1, and 5 mg of vitamin C, and pill 2, which contains 30 IU of vitamin A, 3 mg of vitamin B1, and 20 mg of vitamin C. Pill 1 costs 15¢, and pill 2 costs 45¢. Complete parts a and b below. ... 1. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 4 of pill 1 and 1 of pill 2. The minimum cost is $ 1.05 . Simplify your answers. Type integers or decimals.) o. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. He is receiving 180 IU of vitamin A, 0 mg of vitamin B1, and 0 mg of vitamin C more than he needs. Simplify your answers.) s there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer below. O A. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than needed of another vitamin. O B. Yes. Take one fewer of each pill to reduce the cost. O C. Yes. Reverse the numbers of each pill taken.

contains 90 IU of vitamin A, 3 mg of vitamin B1, and 5 mg of vitamin C, and pill 2, which contains 30 IU of vitamin A, 3 mg of vitamin B1, and 20 mg of vitamin C. Pill 1 costs 15¢, and pill 2 costs 45¢. Complete parts a and b below. ... 1. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 4 of pill 1 and 1 of pill 2. The minimum cost is $ 1.05 . Simplify your answers. Type integers or decimals.) o. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. He is receiving 180 IU of vitamin A, 0 mg of vitamin B1, and 0 mg of vitamin C more than he needs. Simplify your answers.) s there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer below. O A. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than needed of another vitamin. O B. Yes. Take one fewer of each pill to reduce the cost. O C. Yes. Reverse the numbers of each pill taken.

PREALGEBRA
PREALGEBRA
15th Edition
ISBN:9781938168994
Author:OpenStax
Publisher:OpenStax
Chapter9: Math Models And Geometry
Section9.2: Solve Money Applications
Problem 76E: Parent Volunteer Laurie was completing the treasurer’s report for her son’s Boy Scout troop at the...
See similar textbooks
icon
Related questions
Question
A patient takes vitamin pills. Each day he must have at least 210 IU of vitamin A, 15 mg of vitamin B1, and 40 mg of vitamin C. He can choose between pill 1, which contains 90 IU of vitamin A, 3 mg of vitamin B1, and 5 mg of vitamin C, and pill 2, which contains 30 IU of vitamin A, 3 mg of vitamin B,, and 20 mg of vitamin C. Pill 1 costs 15¢, and pill 2 costs 45¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 4 of pill 1 and 1 of pill 2. The minimum cost is $ 1.05. (Simplify your answers. Type integers or decimals.) b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. He is receiving 180 IU of vitamin A, 0 mg of vitamin B1, and 0 mg of vitamin C more than he needs. (Simplify your answers.) Is there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer below. A. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than needed of another vitamin. B. Yes. Take one fewer of each pill to reduce the cost. O C. Yes. Reverse the numbers of each pill taken.
Transcribed Image Text:A patient takes vitamin pills. Each day he must have at least 210 IU of vitamin A, 15 mg of vitamin B1, and 40 mg of vitamin C. He can choose between pill 1, which contains 90 IU of vitamin A, 3 mg of vitamin B1, and 5 mg of vitamin C, and pill 2, which contains 30 IU of vitamin A, 3 mg of vitamin B,, and 20 mg of vitamin C. Pill 1 costs 15¢, and pill 2 costs 45¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 4 of pill 1 and 1 of pill 2. The minimum cost is $ 1.05. (Simplify your answers. Type integers or decimals.) b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. He is receiving 180 IU of vitamin A, 0 mg of vitamin B1, and 0 mg of vitamin C more than he needs. (Simplify your answers.) Is there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer below. A. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than needed of another vitamin. B. Yes. Take one fewer of each pill to reduce the cost. O C. Yes. Reverse the numbers of each pill taken.
A company sells sets of kitchen knives. A Basic Set consists of 2 utility knives and 1 chef's knife. A Regular Set consists of 2 utility knives, 1 chef's knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chef's knife, and 1 slicer. The profit is $40 on a Basic Set, $60 on a Regular Set, and $80 on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef's knives, and 200 slicers. (a) If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit? (b) A consultant for the company notes that more profit is made on a Regular Set than on a Basic Set, yet the result from part (a) recommends making up more Basic Sets than Regular Sets. She is puzzled how this can be the best solution. How would you respond? ..... (a) Find the objective function to be used to maximize profit. Let x, be the number of Basic Sets, let x, be the number of Regular Sets, and let x, be the number of Deluxe Sets. What is the objective function? z= 40 x1 + 60 x2 + 80 x3 (Do not include the $ symbol in your answers.) (a) To maximize profit, the company should make up 100 Basic Sets, 0 Regular Sets, and 200 Deluxe Sets. (Simplify your answers.) The maximum profit is $ 20000 . (Simplify your answer.) (b) Choose the correct answer below. A. The overall profit is most affected by the Deluxe Set. The profit generated by the Basic Set and Regular Set does not significantly contribute to the overall profit. B. The Basic Set requires fewer knives. So, fewer Basic Sets can be made up than Regular Sets. This results in higher overall profit. C. Since the Regular Set requires more knives, it has higher production costs. This will result in less profit than the Basic Set. D. The Basic Set requires fewer knives. So, more Basic Sets can be made up than Regular Sets. This results in higher overall profit.
Transcribed Image Text:A company sells sets of kitchen knives. A Basic Set consists of 2 utility knives and 1 chef's knife. A Regular Set consists of 2 utility knives, 1 chef's knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chef's knife, and 1 slicer. The profit is $40 on a Basic Set, $60 on a Regular Set, and $80 on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef's knives, and 200 slicers. (a) If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit? (b) A consultant for the company notes that more profit is made on a Regular Set than on a Basic Set, yet the result from part (a) recommends making up more Basic Sets than Regular Sets. She is puzzled how this can be the best solution. How would you respond? ..... (a) Find the objective function to be used to maximize profit. Let x, be the number of Basic Sets, let x, be the number of Regular Sets, and let x, be the number of Deluxe Sets. What is the objective function? z= 40 x1 + 60 x2 + 80 x3 (Do not include the $ symbol in your answers.) (a) To maximize profit, the company should make up 100 Basic Sets, 0 Regular Sets, and 200 Deluxe Sets. (Simplify your answers.) The maximum profit is $ 20000 . (Simplify your answer.) (b) Choose the correct answer below. A. The overall profit is most affected by the Deluxe Set. The profit generated by the Basic Set and Regular Set does not significantly contribute to the overall profit. B. The Basic Set requires fewer knives. So, fewer Basic Sets can be made up than Regular Sets. This results in higher overall profit. C. Since the Regular Set requires more knives, it has higher production costs. This will result in less profit than the Basic Set. D. The Basic Set requires fewer knives. So, more Basic Sets can be made up than Regular Sets. This results in higher overall profit.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
PREALGEBRA
PREALGEBRA
Algebra
ISBN:
9781938168994
Author:
OpenStax
Publisher:
OpenStax
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
SEE MORE TEXTBOOKS