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Question 1197832: A high-technology electronics firm needs a special microprocessor for use in a microcomputer it manufactures. Three alternatives have been identified for satisfying its needs. It can
purchase the microprocessors from a supplier at a cost of $10 each. The firm also can purchase
one of two pieces of automated equipment and manufacture the microprocessors. One piece of
equipment costs $80,000 and would have variable costs per microprocessor of $8. A more highly
automated piece of equipment costs $120,000 and would result in variable costs of $5 per unit.
Determine the minimum cost alternative for different ranges of output
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the number of micro processors.
option A:
cost per micro processor = 10 dollars each.
y = 10x would be the cost, with y being the total cost and x being the number of micro processors.
option B:
y = 80,000 + 8x.
option C:
120,000 + 5x.
look for when option A is the smallest.
option A less than option B when 10x < 80,000 + 8x.
subtract 8x from both sides of this equation to get 2x < 80,000.
solve for x to get x = 40,000
option A less than option C when 10x <= 120,000 + 5x.
subtract 5x from both sides of this equation to get 5x < 120,000.
solve for x to get x = 24,000.
what this says is that option A is less than option B or C when x < 24000.
option B less than option C when 80,000 + 8x < 120,000 + 5x.
subtract 5x from both sides of the equation and subtract 80,000 from both sides of the equation to get 3x = 40,000.
solve for x to get x = 13,333.333.....
when x = 13,333, option B is less than option C.
when x = 13,334, option C is less than option B.
this suggests that option A is the cheapest from x = 0 to x < 24000 and option C is the cheapest from x > 24000.
note that option C is cheaper than option B when x = < 13,333.00, option A is cheaper than both of them at that point.
these equations can be graphed as shown below:
let me know if you have any questions.
theo
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