Question

Algebra 1 question :D
Medal + Fan!

Answer 1

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) = 2x^2 - 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?

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.

Answer 2

@jagr2713 mind helping me?

Answer 3

hey @surjithayer :D

Answer 4

The cost of making 0 sandwiches is
C(0)=2(0)2−40(0)+300=
The cost of making 0 burgers is
B(0)=(0)2−30(0)+520=

Answer 5

hi y'all :D

Answer 6

so it's 300 and 520 but that is not one of my options

Answer 7

yeah.. weird?!

Answer 8

how D;

Answer 9

\[x^2-30x+520\] is how i read it

Answer 10

me to

Answer 11

and \[C(x) = 2x^2 - 40x + 300\]

Answer 12

no way? let me try and see if I made a mistake in the writing ok?

Answer 13

@misty1212 when did u start OS

Answer 14

and your job is to find the minimum, which is the same as the vertex

Answer 15

what if the minimum cost is for 1 of each?

Answer 16

not 0?

Answer 17

hold the phone dear, we are not nearly there yet
we have more work to do

Answer 18

ok ok :|

Answer 19

@jagr2713 idk maybe three weeks?

Answer 20

to find the minimum value of a quadratic the first coordinate is \(-\frac{b}{2a}\)

Answer 21

i was wondering b.c ur everywhere lol i would see a question and start typing and ur done already and i am like wow lol :D u work fast

Answer 22

haha... she's good alright :D

Answer 23

for \[C(x) = 2x^2 - 40x + 300\] \(a=2,b=-40\) so \(-\frac{b}{2a}=\frac{40}{4}=10\)

Answer 24

find \(C(10)\) use a calculator

Answer 25

for
\[x^2-30x+520\] \(a=1,b=-30,-\frac{b}{2a}=\frac{30}{2}=15\)

Answer 26

so you can compare them

Answer 27

if C(10) then the equation equals -60

Answer 28

hmmm no

Answer 29

try again

Answer 30

ok

Answer 31

I keep getting -60, mind helping?

Answer 32

http://www.wolframalpha.com/input/?i=2*10^2+-+40*10+%2B+300+

Answer 33

how? 100.... what I am I doing wrong?

Answer 34

messing up inputting it in to the calculator is my guess
your calculator cannot read your mind, use parentheses if needed

Answer 35

or just do the arithmetic without one

Answer 36

yeah... that must be it :)

Answer 37

so would the answer be C then?

Answer 38

and now we are done, because there is only one choice where the cost of sandwiches is $100

Answer 39

it is always C so it is probably C now too

Answer 40

haha... yeah :D thank you so much!

Answer 41

\[\color\magenta\heartsuit\]

Answer 42

nice heart :D

Answer 43

what could @surjithayer be typing for so long? :P

Answer 44

\[B(x)=x^2-3ox+520\]
\[B'(x)=2x-30\]
B'(x)=0 gives 2 x-30=0,x=15
B"(x)=2>0 at x=15
cost of burger is minimum at x=15
or minimum cost of burgers=(15)^2-30*15+520=225-450+520=295
c(x)=2x^2-40x+300
c'(x)=4x-40
c'(x)=0 gives 4x-40=0,x=10
c"(x)=4>0 at x=10
cost of sandwiches is minimum at x=10
and minimum cost of sandwiches=2(10)^2-40*10+300=200-400+300=100