Question 275517: COST ANALYSIS - A plant can manufacture 80 golf clubs per day far a daily cost of $8147 and 100 golf clubs per day for a total daily cost of $9647.
A) Assuming that daily cost and production are linearly related, find the total daily cost of producing X golf clubs.
B) Interpret the slpe of this cost equation.
C) What is the effect of a 1 unit increase in production?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! they can manufacture 80 golf clubs per day at a cost of 8147.
they can manufacture 100 golf clubs per day at a cost of 9647
let x = number of golf clubs manufactured per day.
let y = total cost for manufacturing x golf clubs.
x1,y1 = 80,8147
x2,y2 = 100,9647
y2-y1 = 9647 - 8147 = 1500
x2-x1 = 100-80 = 20
slope intercept form of equation for straight line is y = mx + b where m is the slope and b is the y intercept.
slope = y2-y1 / x2-x1 = 1500/20 = 75
equation becomes y = 75*x + b
take one of the point pairs and solve for b.
use 100,9647
equation becomes:
9647 = 75*100 + b
solve for b to get b = 9647 - (75*100) = 2147
equation becomes:
y = 75*x + 2147
graph of the equation looks like this:
I inserted horizontal lines at y = 8147 and y = 9647.
trace a vertical line from the intersection of those lines with the graph of the equation (slanted line) and you will see that this happens at x = 80 and x = 100 respectively.
answers to the questions are:
A) Assuming that daily cost and production are linearly related, find the total daily cost of producing X golf clubs.
Equation is y = 75*x + 2147
B) Interpret the slope of this cost equation.
Slope is 75.
C) What is the effect of a 1 unit increase in production?
When x goes up by 1, y goes up by 75.
assume x = 100, then y = 75*100 + 2147 = 9647
assume x = 101, then y = 75*101 + 2147 = 9722
9722 - 9647 = 75
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