## Linear Programming

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Nats
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### Linear Programming

A builder is planning to build houses on a 9000m^2 plot of land. Some of the houses will be small. The others will be large. The number of small houses is represented by S. The number of large houses are represented by L. The authorities insist that there must be more small houses than large houses, and there must be at least 6 large houses.

a) write down two algebraic inequalities for these two conditions

Each small house requires 300m^2 of land and each large house requires 500m^2 of land .

I think the answers are: L is greater than or equal to 3000m^2 (first condition, since there must be at least 6 large houses) and 6L + S less than or equal to 9000m^2 (second condition) Is this correct?

b) use the fact that the plot of land has a total area of 9000m^2 to show that 3S + 5L is less than or equal to _< 90

but 3S = 3 X 300 = 900 and 5L 5 x 500 = 2500. we have a total of 3400. so how can 3400 be less than or equal to 90?

nona.m.nona
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### Re: Linear Programming

The number of small houses is represented by S. The number of large houses are represented by L....

Each small house requires 300m^2 of land and each large house requires 500m^2 of land .

I think the answers are: L is greater than or equal to 3000m^2 (first condition, since there must be at least 6 large houses) and 6L + S less than or equal to 9000m^2 (second condition) Is this correct?
I'm sorry, but I do not follow your reasoning. It appears that you have attempted to include at least three different conditions in one equation or inequality. It would likely be more helpful to work in an orderly fashion, clearly stating one's reasoning and processing the information step-by-step.

a) For what does each variable stand?
b) What minimums then must (logically) apply to the variables?
c) What inequality is required by what the "authorities insist" be true?
d) As a result of the other requirement upon which the "authorities insist", how may the original minimum for "L" be revised?

The statements in (c) and (d) are the first two answers.

e) Each "large" requires "500" units of space. What expression then represents the number of units of space required by "L" "larges"?
f) Each "small" requires "300" units of space. What expression then represents the number of units of space required by "S" "smalls"?
g) What statement then represents the total number of units of space required by all the houses?
h) What inequality results from the restriction on the total space available?
i) What inequality results from dividing the inequality in (h) by 100?

Nats
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Joined: Mon Aug 19, 2013 11:14 am
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### Re: Linear Programming

I'm sorry, but I do not follow your reasoning. It appears that you have attempted to include at least three different conditions in one equation or inequality. It would likely be more helpful to work in an orderly fashion, clearly stating one's reasoning and processing the information step-by-step.

a) For what does each variable stand?
b) What minimums then must (logically) apply to the variables?
c) What inequality is required by what the "authorities insist" be true?
d) As a result of the other requirement upon which the "authorities insist", how may the original minimum for "L" be revised?

The statements in (c) and (d) are the first two answers.

e) Each "large" requires "500" units of space. What expression then represents the number of units of space required by "L" "larges"?
f) Each "small" requires "300" units of space. What expression then represents the number of units of space required by "S" "smalls"?
g) What statement then represents the total number of units of space required by all the houses?
h) What inequality results from the restriction on the total space available?
i) What inequality results from dividing the inequality in (h) by 100?
thank you so much @nona

a) L= large house S=small houses
b) minimum of 6 Large houses.
c) I'm not sure : 6L greater than 9000m^2
d) I really dont know :(

e)3000
f)6000
g)9000
h) i dont know?
i) i dont know?

buddy
Posts: 197
Joined: Sun Feb 22, 2009 10:05 pm
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### Re: Linear Programming

a) For what does each variable stand?
a) L= large house S=small houses
unclear. try something like "L: the number of 'large' houses" etc etc
b) What minimums then must (logically) apply to the variables?
b) minimum of 6 Large houses.
no: can you have negative numbers of houses?
c) What inequality is required by what the "authorities insist" be true?
c) I'm not sure....
its in the question: "The authorities insist that there must be more small houses than large houses...": S > ????
d) As a result of the other requirement upon which the "authorities insist", how may the original minimum for "L" be revised?
d) I really dont know :(
its in the question: "...and there must be at least 6 large houses": L >= ????
e) Each "large" requires "500" units of space. What expression then represents the number of units of space required by "L" "larges"?
e)3000
so if theres 1 or 2 or 3 or however, theres always only 3000 units of space????
f) Each "small" requires "300" units of space. What expression then represents the number of units of space required by "S" "smalls"?
f)6000
same Q as for (e)
g) What statement then represents the total number of units of space required by all the houses?
g)9000
do a stmt (not just a number) that uses S & L
h) What inequality results from the restriction on the total space available?
h) i dont know?
this is where you use the number 9000

Nats
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Joined: Mon Aug 19, 2013 11:14 am
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### Re: Linear Programming

Firstly, thank you very much @buddy.

OK, Im getting super, super frustrated, and Im sure you think Im super dumb, but I'll just keep trying till I get it right and hopefully you'll keep helping me till I do.

2nd attempt @nona's reasoning and processing step-by-step with @buddy's replies.

a) For what does each variable stand?
L: the number of large houses
S: the number of small houses

b) What minimums then must (logically) apply to the variables?

6L + S is greater than or equal to 9000m^2
S is greater than or equal to - 6l + 9000m^2

c) What inequality is required by what the "authorities insist" be true?
S greater than L

d) As a result of the other requirement upon which the "authorities insist", how may the original minimum for "L" be revised?
L is greater than or equal to 6

The statements in (c) and (d) are the first two answers.

Answer for a: so the two inequalities for these conditions are: S is greater than L and L is greater than or equal to 6. Is that correct?

e) Each "large" requires "500" units of space. What expression then represents the number of units of space required by "L" "larges"?
L is equal to 500

f) Each "small" requires "300" units of space. What expression then represents the number of units of space required by "S" "smalls"?
S is equal to 300

g) What statement then represents the total number of units of space required by all the houses?
S + L is greater than or equal to 9000

h) What inequality results from the restriction on the total space available?
S greater than 6L is greater than oor equal to 9000

i) What inequality results from dividing the inequality in (h) by 100?
why do we divide by 100?

still not sure of the answer for b.