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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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
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