Find the formula for cost

Question

The manager of a restaurant found that the cost to produce 200 cups of coffee is $20.13, while the cost to produce 400 cups is $38.93. Assume the cost C(x) is a linear function of x, the number of cups produced.

 

a) Find the formula for C(x)

 

b) What is the fixed (initial cost)

 

c) Find the total cost of producing 1200 cups

Answer 1

Cost is a function of number of cups provided.

We have two points:  (200, 20.13), (400, 38.93)

 

Find the slope: m = (change in y)/(change in x)

m = (38.93-20.13)/(400-200) = 18.80/200 = 0.094

 

c(x) = 0.094x + b   where b is the y intercept

 

Let's use (200, 20.13) as (x, y) to find b

 

20.13 = 0.094(200) + b

20.13 = 18.8 + b

20.13 - 18.8 = b

1.33 = b

 

c(x) = 0.094x + 1.33

 

The fixed initial cost is the amount you spend if you haven't

yet produced any cups of coffee... x=0... The fixed initial cost is $1.33

 

To find the total to produce 1200 cups just replace x with 1200

in our c(x) equation and do the calculation.