SOLUTION: a small company finds that it costs $3,200 to produce 100 units per day and $9,600 to produce 500 units per day a) assuming the relationship between cost and number of units pro

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Question 336560: a small company finds that it costs $3,200 to produce 100 units per day and $9,600 to produce 500 units per day
a) assuming the relationship between cost and number of units produced per day is linear. find a linear equation that expresses the cost as a function of the number of units produced per day.
b) how many units per day can the company produce for $10,000?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a small company finds that it costs $3,200 to produce 100 units per day and
$9,600 to produce 500 units per day
:
a) assuming the relationship between cost and number of units produced per day is linear.
find a linear equation that expresses the cost as a function of the number of
units produced per day.
:
Find the slope using the slope formula; m = %28y2-y1%29%2F%28x2-x1%29
Assign the given values as follow
x1=100, y1=3200
x2-500, y2=9600
m = %289600-3200%29%2F%28500-100%29 = %286400%29%2F%28400%29 = 16 is the slope
:
Use the point/slope formula to find the equation: y - y1 = m(x - x1)
y - 3200 = 16(x - 100)
y - 3200 = 16x - 1600
y = 16x - 1600 + 3200
y = 16x + 1600
Cost equation
f(x) = 16x + 1600, where x = no. of unit produced per day
:
b) how many units per day can the company produce for $10,000?
16x + 1600 = 10000
16x = 10000 - 1600
16x = 8400
x = 8400/16
x = 525 units cost $10000