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A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.
Food I : A = 2 , B = 1, C = 1, D = 2
Foof II : A = 1, B = 1, C = 2 ,D = 3
Assuming x units of food I is to be mixed with y units of food II the situation can be expressed as
Food I : A = 2 , B = 1, C = 1, D = 2
Foof II : A = 1, B = 1, C = 2 ,D = 3
Assuming x units of food I is to be mixed with y units of food II the situation can be expressed as
- a)2x + y ≤ 9
x + y ≤ 7
x + 2y ≤ 10
2x+ 3 y ≤ 12
x > 0, y > 0 - b)2x + y ≥ 30
x + y ≤ 7
x + 2y ≥ 10
x + 3y ≥ 12 - c)2x + y ≥ 9
x + y ≥ 7
x + y ≤ 10
x + 3y ≥ 12 - d)2x + y ≥ 9
x + y ≥ 7
x + 2 y ≥ 10
2x + 3 y ≥ 12
x ≥ 0 , y ≥ 0,
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A dietitian wishes to mix together two kinds of food so that the vitam...
We can set up the following system of inequalities to represent the given constraints:
2x + y ≥ 9
x + y ≥ 7
x + 2y ≥ 10
2x + 3y ≥ 12
We want to find the values of x and y that satisfy all of these inequalities and minimize the amount of food used (i.e. minimize x+y).
One approach to solve this type of problem is to graph the inequalities and find the feasible region, which is the region that satisfies all of the constraints. The optimal solution will be at one of the vertices of the feasible region. However, since we have four inequalities, graphing them can be time-consuming and not very accurate.
Another approach is to use linear programming, which is a method for optimizing a linear objective function subject to linear constraints. In this case, our objective function is x+y (the total amount of food used). We want to minimize this function subject to the constraints given by the four inequalities.
We can use a software program or a calculator that has a linear programming function to solve this problem. For example, using the Solver add-in in Microsoft Excel, we can set up the problem as follows:
Objective: Minimize x+y
Subject to:
2x + y ≥ 9
x + y ≥ 7
x + 2y ≥ 10
2x + 3y ≥ 12
x ≥ 0
y ≥ 0
Solving this problem using the Simplex algorithm, we get the optimal solution:
x = 2.4 Kg of food I
y = 4.6 Kg of food II
The total amount of food used is x+y = 7 Kg.
Therefore, to meet the vitamin requirements, the dietitian should mix 2.4 Kg of food I with 4.6 Kg of food II, and the total amount of food used will be 7 Kg.
2x + y ≥ 9
x + y ≥ 7
x + 2y ≥ 10
2x + 3y ≥ 12
We want to find the values of x and y that satisfy all of these inequalities and minimize the amount of food used (i.e. minimize x+y).
One approach to solve this type of problem is to graph the inequalities and find the feasible region, which is the region that satisfies all of the constraints. The optimal solution will be at one of the vertices of the feasible region. However, since we have four inequalities, graphing them can be time-consuming and not very accurate.
Another approach is to use linear programming, which is a method for optimizing a linear objective function subject to linear constraints. In this case, our objective function is x+y (the total amount of food used). We want to minimize this function subject to the constraints given by the four inequalities.
We can use a software program or a calculator that has a linear programming function to solve this problem. For example, using the Solver add-in in Microsoft Excel, we can set up the problem as follows:
Objective: Minimize x+y
Subject to:
2x + y ≥ 9
x + y ≥ 7
x + 2y ≥ 10
2x + 3y ≥ 12
x ≥ 0
y ≥ 0
Solving this problem using the Simplex algorithm, we get the optimal solution:
x = 2.4 Kg of food I
y = 4.6 Kg of food II
The total amount of food used is x+y = 7 Kg.
Therefore, to meet the vitamin requirements, the dietitian should mix 2.4 Kg of food I with 4.6 Kg of food II, and the total amount of food used will be 7 Kg.
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A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer?
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A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer?.
A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer?.
Solutions for A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
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Here you can find the meaning of A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A dietitian wishes to mix together two kinds of food so that the vitamin content of the mixture is at least 9 units of vitamin A, 7 units of vitamin B, 10 units of vitamin C and 12 units of vitamin D. The vitamin content per Kg. of each food is shown below.Food I : A = 2 , B = 1, C = 1, D = 2Foof II : A = 1, B = 1, C = 2 ,D = 3Assuming x units of food I is to be mixed with y units of food II the situation can be expressed asa)2x + y ≤ 9x + y ≤ 7x + 2y ≤ 102x+ 3 y≤12x > 0, y > 0b)2x + y ≥ 30x + y ≤ 7x + 2y ≥ 10x + 3y ≥ 12c)2x + y ≥ 9x + y ≥ 7x + y ≤ 10x + 3y ≥ 12d)2x + y ≥ 9x + y ≥ 7x + 2 y ≥ 102x + 3 y ≥ 12x ≥ 0 , y ≥ 0,Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
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