Question

A factory is currently running at 85% of its original capacity, and management is considering upgrading the equipment.

The upgrade will take 6 months, during which time the factory will not run at all. Once complete, the factory’s output will increase to 120% of the original capacity. After how long would the upgraded factory’s production match the current 85% production? In other words, how long will it take for the factory to make up for the loss of 6 months?

(Hint: The problem can be solved using a system of equations, but any method is acceptable as long as it is justified. If you get stuck, try letting the factory’s original output be 100 units per month.)

PLEASE SERIOUS ANSWERS ONLY. I would appreciate work shown!

Answer 1

I will take the sugestion, so 85 units per month (100 is full capacity)


so while doing maintinance, the 6 months is wasted, 0 ouput, basically 85*6=510 lost

now we have to see how many months x it takes for the output to match

the output that would have been is
510+85x
the output now is 120x
so
510+85x=120x
minus 85x both sides
510=35x
divide both sides by 35
14.57=x
round up
15 months needed