What is the equation that models the cost function?

Question

A company buys and sells baseball caps. the total cost function is linear, the total cost of 200 caps is $2680, and the total cost of 500 caps is $3500. write the equation that models this cost function.

Answer 1

If you think of x as the number of caps and y and the cost, then this is just like asking to find the line that goes through the two points (200, 2680) and (500, 3500).

 

The slope of the line is the cost per hat, and the y-intercept is the fixed initial cost.  

 

So the slope is (3500 - 2680) / (500 - 200) = 820 / 300 = 41/15.

 

So using the usual way to find the y-intercept, you have y = 41/15 x + b.

 

Pick one of the points to find b:

 

3500 = (41/15) * 500 + b

3500 - (41/15) * 500 = b

 

2133.33 = b

 

Rounding 41/15 gives the cost per hat of $2.73

 

So the cost equation is y = 2.73 x + 2133.33