Matt sells burgers and sandwiches. The daily cost of making burgers is $520 more than the difference between the square of the number of burgers sold and 30 times the number of burgers sold. The daily cost of making sandwiches is modeled by the following equation:
C(x) = 2x2 - 40x + 300
C(x) is the cost in dollars of selling x sandwiches.
Which statement best compares the minimum daily cost of making burgers and sandwiches

- anonymous

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- anonymous

It is greater for sandwiches than burgers because the approximate minimum cost is $250 for burgers and $292 for sandwiches.
It is greater for sandwiches than burgers because the approximate minimum cost is $100 for burgers and $295 for sandwiches.
It is greater for burgers than sandwiches because the approximate minimum cost is $295 for burgers and $100 for sandwiches.
It is greater for burgers than sandwiches because the approximate minimum cost is $292 for burgers and $250 for sandwiches

- anonymous

@triciaal HELP ?

- triciaal

I am helping !
this is what I have so far

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## More answers

- triciaal

|dw:1432963888967:dw|

- triciaal

|dw:1432964031859:dw|

- triciaal

the equation written with the question is for sandwiches when x = 0 then the cost = 300

- anonymous

I Dont understand

- anonymous

@Jack1 help ?

- Jack1

tricalls back, she's doin awesome man, jus be patient

- triciaal

|dw:1432964510506:dw|

- triciaal

sorry, i'm missing something (more than just sleep)

- Jack1

want a hand?

- triciaal

what is the value of x when the costs are equal
@Jack1 sure always feel free to join in

- anonymous

So, the answer is:
It is greater for burgers than sandwiches because the approximate minimum cost is $292 for burgers and $250 for sandwiches
because it is about 1/2 the total when I make x=0 ? @triciaal & @Jack1

- Jack1

not the correct answer

- anonymous

ok

- Jack1

The daily cost (C(z))of making burgers (z) is $520 more than the difference between the square of the number of burgers (z^2) sold and 30 times the number of burgers sold (30z).
so as an equation for burgers:
C(z) = z^2 - 30z + 520

- Jack1

The daily cost of making sandwiches is:
C(x) = 2x^2 - 40x + 300

- triciaal

compare the cost when x = 4?

- Jack1

cost (C) to make sandwiches (x)
\(\large C(x) = 2x^2 - 40x + 300\)
this equation is a parabola,
lowest cost is at lowest point on parabola = turning point
turning point is when the gradient = 0
gradient of a parabola is the derivative
\(\large C(x) = 2x^2 - 40x + 300\)
\(\large C'(x) = 4x - 40 \)
so when gradient ( C'(x) ) = 0
\(\large 0 = 4x - 40 \)
\(\large 40 = 4x \)
\(\large x = 10 \)
so lowest cost is when x = 10 (number of sandwiches = 10)
what cost (C) is that tho?
\(\large C(x) = 2x^2 - 40x + 300\)
\(\large C(10) = 2(10)^2 - 40(10) + 300\)
\(\large C = u solve this ???\) @zayyyc_

- Jack1

then do the same for burgers (z)
then you'll have ur answer ;)

- triciaal

@Jack1 so 10 sandwiches and 4 burgers?

- Jack1

i got 15 burgers for that parabola min point...?

- anonymous

me to @Jack1

- triciaal

for burgers yes 15

- Jack1

cool @zayyyc_ so what did u get as the min cost for sangers, and whats the min cost for burgers?

- triciaal

got it 295

- triciaal

|dw:1432965929266:dw|

- Jack1

yep, me too: $295 for 15 burgers is it's min, and $100 for 10x sandwiches is it's minimum cost... hope this helps?

- anonymous

It is greater for sandwiches than burgers because the approximate minimum cost is $250 for burgers and $292 for sandwiches ?

- anonymous

@Jack1

- Jack1

nah man, sorry
we know the min cost for sandwiches is $100
and the min cost for burgers is $295
so the only one that fits is C, yeah?
It is greater for burgers than sandwiches because the approximate minimum cost is $295 for burgers and $100 for sandwiches.

- Jack1

you following ok tho or need something explained a bit more?
s 'cool if u do hey

- anonymous

i got it thank you

- Jack1

cool, props ;)

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