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

Answer:

$y = 25x +1950$

Step-by-step 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)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{3200 - 2700}{50 - 30}$

$m = \frac{500}{20}$

$m = 25$

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

$y = 25x - 750 + 2700$

$y = 25x +1950$