Question

PLEASE HELP :) The manager of a restaurant found that the cost of producing 100 cups of coffee is $11.02, while the cost of producing 400 cups is $40.12. Assume that the cost C(x) is a linear function of x, the number of cups produced.
A. Find a formula for C(x)

Answer 1

Let

x = number of cups
y = cost

"the cost of producing 100 cups of coffee is $11.02"

so we know x = 100 and y = 11.02. We have one point (100,11.02)

we're also told "the cost of producing 400 cups is $40.12"

this means x = 400, y = 40.12. The other point is (400, 40.12)

Answer 2

What is the slope of the line through (100,11.02) and (400, 40.12) ?

Answer 3

Is it -.023? That's what I calculated :/ @jim_thompson5910

Answer 4

OOps made a mistake, I will redo that!

Answer 5

that's incorrect

Answer 6

alright

Answer 7

.097! @jim_thompson5910

Answer 8

correct

Answer 9

that's the slope

Answer 10

Plug in the slope m = 0.097 and the point (x,y) = (100,11.02) into y=mx+b and solve for b


y = mx + b

y = 0.097x + b

11.02 = 0.097*100 + b ... plug in x = 100 and y = 11.02

11.02 = 9.7 + b

b = ???

Answer 11

1.32! @jim_thompson5910

Answer 12

m = 0.097
b = 1.32

Answer 13

y = mx+b

y = 0.097x+b

y = 0.097x+1.32

Answer 14

Then you replace y with C(x) to turn it into a function

y = 0.097x+1.32

C(x) = 0.097x+1.32

Answer 15

so that's your cost function

Answer 16

Plug in x = 100 and tell me what you get

Answer 17

11.02 :) @jim_thompson5910

Answer 18

Thank you so very much! You're very helpful and I appreciate it greatly :)

Answer 19

you're welcome

and I recommend you also check x = 400

Answer 20

40.12 :) Thanks!

Answer 21

you're welcome