# Restrictions on variables.

• Kirito123
I think you should go back to your original answer, with the two constraints ##30c + 40b \leq 3000## and ##b,c \geq 0##.The restrictions for the variables c and b are that they must be greater than or equal to 0, since you cannot have a negative number of meals. Additionally, the total cost of the meals cannot exceed $3000, so the equation 30c + 40b = 3000 represents this constraint. Therefore, the restrictions on the variables are 0 ≤ c and 0 ≤ b, and the equation 30c + 40b = 3000. Kirito123 ## Homework Statement Jeffrey is planning a large dinner party. His budget is$3000. He has the option of serving chicken at $30 per meal or roast beef at$40 per meal.

The cost of the party can be modeled with the equation
30c + 40b = 3000, where c represents the number of chicken meals ordered and
b represents the number of roast beef meals ordered.

What are the restrictions on the variables? Justify your reasoning.

## Homework Equations

restrictions on variables.

## The Attempt at a Solution

Well for the variable c you cannot exceed 100 meals or you will exceed your budget and you cannot have – 1 or more meals/$. So it has to be 0 or greater. So you can say: 0 <_ C <_ 3000 ($) (Note: the <_ is meant to represent greater or equal to.)Same with b you cannot exceed 75 beef meals or you u will exceed your budget. You also can’t have –1 meals or dollars. So we can say that it has to be 0 or greater.

0 <_ B <_ 3000 ($)Its a new concept for me and I would like to know if I am understanding it correctly, and got the answer right. I appreciate your time and effort and would like to say thank you in advance. Kirito123 said: ## Homework Statement Jeffrey is planning a large dinner party. His budget is$3000. He has the option of serving chicken at $30 per meal or roast beef at$40 per meal.

The cost of the party can be modeled with the equation
30c + 40b = 3000, where c represents the number of chicken meals ordered and
b represents the number of roast beef meals ordered.

What are the restrictions on the variables? Justify your reasoning.

## Homework Equations

restrictions on variables.

## The Attempt at a Solution

Well for the variable c you cannot exceed 100 meals or you will exceed your budget and you cannot have – 1 or more meals/$. So it has to be 0 or greater. So you can say: 0 <_ C <_ 3000 ($) (Note: the <_ is meant to represent greater or equal to.)Same with b you cannot exceed 75 beef meals or you u will exceed your budget. You also can’t have –1 meals or dollars. So we can say that it has to be 0 or greater.

0 <_ B <_ 3000 ($)Its a new concept for me and I would like to know if I am understanding it correctly, and got the answer right. I appreciate your time and effort and would like to say thank you in advance. Are you sure you have presented the problem correctly? There are two possibilities, (a) and (b) below. (a) If Jeffrey can spend at most$3000, then the constraint should be ##30 c + 40 b \leq 3000##, and, of course, ##b, c \geq 0##.

(b) If Jeffrey must spend exactly $3000, then the constraint is as you have written it: ##30 c + 40 b = 3000##, and, of course, ##b,c \geq 0##. Ok I think I get what your saying, Jeffrey doesn't have to spend exactly$3000. He just can't spend more then that budget. So I am guessing that the answer (a) that you suggested is right, since Jeffrey can only spend at most $3000. Also how would I explain that in steps?? i don't understand what to do? is my answer correct? I came up with another answer: please tell me if this is correct! Assuming that Jeffrey is purchasing both chicken and roast beef, but only has a budget of$3000, the budget should be divided amongst both chicken and beef meals. For chicken meals, it cannot exceed 50 meals, or this would surpass $1500 dollars. And for beef it cannot exceed around 37 meals, or this would exceed$1500.

Restriction for chicken meals: 0 < C < 1500 ($) Restriction for beef meals: 0 < B < 1500($)

Therefore the constraint should be: 30c + 40b < 3000 and b, c > 0

Kirito123 said:
I came up with another answer: please tell me if this is correct!
Assuming that Jeffrey is purchasing both chicken and roast beef, but only has a budget of $3000, the budget should be divided amongst both chicken and beef meals. For chicken meals, it cannot exceed 50 meals, or this would surpass$1500 dollars. And for beef it cannot exceed around 37 meals, or this would exceed $1500. Restriction for chicken meals: 0 < C < 1500 ($)

Restriction for beef meals: 0 < B < 1500($) Therefore the constraint should be: 30c + 40b < 3000 and b, c > 0 In your original post, you had 30c+40b=3000. It reads as though you were given that equation as part of the problem specification. Is that so, or did you make up that equation based on the$3000 budget?

haruspex said:
In your original post, you had 30c+40b=3000. It reads as though you were given that equation as part of the problem specification. Is that so, or did you make up that equation based on the $3000 budget? I made it up based on the$3000 budget.

Kirito123 said:
I came up with another answer: please tell me if this is correct!
Assuming that Jeffrey is purchasing both chicken and roast beef, but only has a budget of $3000, the budget should be divided amongst both chicken and beef meals. For chicken meals, it cannot exceed 50 meals, or this would surpass$1500 dollars. And for beef it cannot exceed around 37 meals, or this would exceed $1500. Restriction for chicken meals: 0 < C < 1500 ($)

Restriction for beef meals: 0 < B < 1500($) Therefore the constraint should be: 30c + 40b < 3000 and b, c > 0 The restrictions ##30 c + 40 b \leq 3000##, ##b,c \geq 0## are correct. The restrictions to$1500 for each are incorrect. Presumably, Jeffrey can spend $3000 on chicken and$0 on beef, or $3000 on beef and$0 on chicken. The only real restriction given in the problem as written is either that he cannot spend more than $3000 in total, or else must spend exactly$3000 in total (depending on the precise interpretation). Of course, he cannot spend negative amounts, so you also need ##b,c \geq 0##.

If, in fact, there are additional restrictions on Jeffrey's spending patterns (such as a $1500 limit on each of beef and chicken) then those must be stated as part of the problem's description. It is not valid to simply add them later for no really good reason. I see. So basically since they did not give us like you have to spend this much on beef or chicken etc. then my formula i mentioned was wrong. But since i can spend only up to 3000 dollars on beef or chicken that's why its 30c + 40b < 3000. that means both chicken and beef can not pass 3000 in total. correct? what do you mean by that? Kirito123 said: what do you mean by that? Sorry, forget it. I misread your post. Too hasty. Ok lol Kirito123 said: So basically since they did not give us like you have to spend this much on beef or chicken etc. then my formula i mentioned was wrong. But since i can spend only up to 3000 dollars on beef or chicken that's why its 30c + 40b < 3000. that means both chicken and beef can not pass 3000 in total. correct? Yes, we have already said that. That means that 30c + 40b <= 3000, NOT "< 3000". If you said "< 3000" you would be saying "<= 2999.99", so you would be allowing Jeffrey to spend any amount up to$2999.99, but he would not be allowed to spend one more penny to bring it up to \$3000.

Ok i got it thanks for the help :)

I do not see the other restriction that both b and c must be positive integers.

ehild said:
I do not see the other restriction that both b and c must be positive integers.

Well, non-negative integers at least.

## 1. What are restrictions on variables?

Restrictions on variables refer to limitations or conditions that are placed on the values that a variable can take. These restrictions can be imposed for various reasons, such as to ensure the validity of a mathematical equation or to limit the scope of a study.

## 2. Why are restrictions on variables important?

Restrictions on variables are important because they help to ensure that the results of a study or experiment are accurate and reliable. By limiting the range of values that a variable can have, researchers can control for potential confounding factors and better understand the relationship between variables.

## 3. What are some common types of restrictions on variables?

Some common types of restrictions on variables include upper and lower bounds, equality constraints, and fixed values. Upper and lower bounds limit the range of values that a variable can take, while equality constraints require the variable to be equal to a specific value. Fixed values, on the other hand, restrict the variable to a single value throughout the study or experiment.

## 4. How do restrictions on variables impact data analysis?

Restrictions on variables can have a significant impact on data analysis. For example, if a variable is restricted to a specific range of values, it may affect the distribution of the data and the types of statistical tests that can be used. In addition, restrictions on variables can also affect the interpretation of results and the generalizability of the findings.

## 5. What are some potential challenges of working with restrictions on variables?

One of the main challenges of working with restrictions on variables is finding the right balance between controlling for potential confounding factors and allowing for enough variability in the data. In addition, restrictions on variables may also make it more difficult to generalize the results to a larger population. Finally, researchers must also ensure that the restrictions are clearly communicated and understood in order to avoid any misinterpretation of the results.

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