Question

Application of Linear Function

Problem: Dunkin Donuts
found that the cost to produce 100 cups of coffee is
$11.02, while the cost to produce 400 cups is $40.12.
Assume the cost C(x) is a linear function of x, the number
of cups produced
(a) Find a formula for C(x).
(b) What is the fixed cost?
(c) Find the total cost of producing 1001 cups.
(d) Find the marginal cost of any cup and what does this
mean to the manager?

Answer 1

see below

Explanation:

Find the slope

m= ( 40.12 - 11.02)/ (400-100)

= 29.1 / 300

=.097

We can use the linear form y = mx+b

y =.097x +b

40.12 = .097 ( 400) +b

40.12 = 38.80 +b

1.32 = b

y = 0.097x + b

C(x) = .097x + 1.32

The fixed cost is b = 1.32

C(1001) = .097(1001) + 1.32

=98.417

The marginal cost is the cost of adding one more item, which is the slope

.097 is the marginal cost

It means to make one more cup of coffee will cost $.097