Question 1196258: The manager of a restaurant found that the cost to produce 50 cups of coffee is
$ 9.00, while the cost to produce 350 cups is $39.00. Assume the relationship between the cost y to produce x cups of coffee is linear.
a. Write a linear equation that expresses the cost, y, in terms of the number of cups of coffee, x.
b. How many cups of coffee are produced if the cost of production is $
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of cups of coffee
y = total cost in dollars
50 cups cost $9, meaning: x = 50 and y = 9
I.e. the point (x,y) = (50, 9) is on the line
Another point is (350, 39) since 350 cups cost $39 to produce.
Let's find the slope of the line through (50,9) and (350,39)
(x1,y1) = (50,9) and (x2,y2) = (350,39)
m = (y2 - y1)/(x2 - x1)
m = (39 - 9)/(350 - 50)
m = 30/300
m = 1/10
m = 0.10
The slope of 0.10 means that each time x goes up by 1, y increases by 0.10
Each new cup of coffee costs $0.10, i.e. 10 cents
Now apply point slope form.
y - y1 = m(x - x1)
y - 9 = 0.10(x - 50)
y - 9 = 0.10x - 0.10*50
y - 9 = 0.10x - 5
y = 0.10x - 5+9
y = 0.10x + 4
The equation is in y = mx+b form
m = 0.10 = slope
b = 4 = y intercept
The slope tells us how much each extra cup costs
The y intercept is the starting cost. If zero cups are produced, there is still a fixed fee of $4 to set everything up. Think of it like a fee to get in the door.
All of the work/steps shown above apply to part (a) only.
----------------------------------
Part (b) cannot be answered since the cost of production has been cut off.
You'll need to revise your post to include this value.
I'll go over a hypothetical example
Let's say the cost of production is $100
This means we plug in y = 100 and solve for x.
y = 0.10x + 4
0.10x + 4 = y
0.10x + 4 = 100
0.10x = 100-4
0.10x = 96
x = 96/(0.10)
x = 960
Therefore, a production cost of $100 means that 960 cups were produced.
Once again, this is a hypothetical example. Follow steps similar to this with the actual cost your teacher gave you.
|
|
|
