Question

The manager of a restaurant found that the cost to produce 200 cups of coffee is ​$20.15​, while the cost to produce 500 cups is ​$548.35. Assume the cost​ C(x) is a linear function of​ x, the number of cups produced. Answer parts a through f.

a. Find a formula for​ C(x).

Answer 1

C(x)=1.76067x - 331.98

Explanation:

We are given two points (x,y) of the linear function C(x):

P1 = (200; 20.15) and P2 = (500; 548.35)

The slope of the function, 'm', can be found by:

`m = (y_1-y_2)/(x_1-x_2) \\m = (548.35-20.15)/(500-200)\\m= 1.7607`

Applying point P1 to the general linear equation gives us C(x):

`(C-C_1) = m(x-x_1)\\C-20.15=1.76067(x-200)\\C(x)=1.76067x - 331.98`