Question

a coffee supplier finds that it cost $850 to roast and package 100 pounds of coffee in a day and $2850 to produce 500 pounds of coffee in a day. assume that the cost function is linear. express the cost as a function of the number of pounds of coffee they produce each day

Answer 1

f(x) = 5x + 350

Explanation:

Create 2 points using the information given, where x is the number of pounds of coffee and y is the cost.

The 2 points are (100, 850) and (500, 2850)

Then, use rise over run to find the slope:

(y2 - y1) / (x2 - x1)

(2850 - 850) / (500 - 100)

2000 / 400

= 5

Then, plug in the slope and a point into y = mx + b to find b:

y = mx + b

850 = 5(100) + b

850 = 500 + b

350 = b

Plug in the slope and y intercept into y = mx + b to get the equation:

y = 5x + 350

Put it into function form:

f(x) = 5x + 350 is the cost function