Question

The manager of a restaurant found that the cost to produce 100 cups of coffee is ​$10.62​, while the cost to produce 600 cups is ​$57.12. 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). ​C(x)equals nothing ​(Use integers or decimals for any numbers in the​ expression.)

Answer 1

`C(x) = 0.093x+1.32`

Explanation:

Given that the manager of a restaurant found that the cost to produce 100 cups of coffee is ​$10.62​, while the cost to produce 600 cups is ​$57.12.

Also given that C(x) can be assumed as linear.

Hence we can treat cups X as independent variable and Y the cost for that

Slope of the line = change in y/change in x=
`(57.12-10.62)/(600-100) \\=0.093`

Take one point and use slope point formula for lines

`y-y_1=m(x-x_1)\\y-10.62 = 0.093(x-100)\\y= 0.093x+1.32`

Change y to C(x)

`C(x) = 0.093x+1.32`