Question 1190204: A small producer of machine tools wants to move to a larger building, and has identified two alternatives. Location A has annual fixed costs of $160,000 and variable costs of $15,000 per unit; location B has annual fixed costs of $360,000 and variable costs of $14,000 per unit. The finished items sell for $16,000 each.
Question: what volume of output would the two locations have the same total cost?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of units produced
y = total cost in thousands of dollars
eg: y = 5 means the total cost is 5000 dollars
Cost equations:
Location A: y = 15x + 160
Location B: y = 14x + 360
The general template is
total cost = (variable cost)*x + (fixed cost)
Since we want the two costs to be the same, we're dealing with the same y value.
Apply substitution and solve for x.
y = 14x+360
15x+160 = 14x+360
15x-14x = 360-160
x = 200
You need to produce 200 units to get the same cost for each location.
Location A:
y = 15x+160
y = 15*200+160
y = 3,000+160
y = 3,160
Location B:
y = 14x+360
y = 14*200+360
y = 2,800+360
y = 3,160
Getting the same result for y helps confirm the correct x value.
Remember that y is the total cost in thousands. So we multiply that y value by 1000 to get 1000*3160 = 3,160,000
Each location will have a total cost of $3,160,000
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Answer: 200 units
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