Question

To manufacture 30 items, it costs $2700, and to manufacture 50 items, it costs $3200. If x represents the number of items manufactured and y the cost, write the cost function.

a. Y= -25X + 4450
b. Y = 500 X 21,800
c. Y = 0.04X + 3198
d. Y = 25X + 1950

Answer 1

`y = 25x +1950`

Explanation:

Given

`(x_1,y_1) = (30,2700)`

`(x_2,y_2) = (50,3200)`

Required

Determine the linear function

We start by calculating the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

So, we have:

`m = (3200 - 2700)/(50 - 30)`

`m = (500)/(20)`

`m = 25`

The equation is then calculated as:

`y - y_1 = m(x - x_1)`

This gives:

`y - 2700 = 25(x - 30)`

`y - 2700 = 25x - 750`

Make y the subject

`y = 25x - 750 + 2700`

`y = 25x +1950`