A manufacturing company plans to progressively increase its production capacity over the next few quarters. (A quarter is a peri
od of three months.) The increase in production can be modeled by the equation y = x6 − 25x4 + 199x2, where x is the number of quarters. What is the minimum duration required for the company to reach a production capacity of 4,975 units?
1 answer:
Answer:
5 months
Step-by-step explanation:
We assume that y represents production capacity, rather than <em>increase</em> in production capacity. Then we want to solve the 6th-degree equation ...
x^6 -25x^4 +199x^2 -4975 = 0
This can be factored in groups as ...
x^4(x^2 -25) + 199(x^2 -25) = 0
(x^4 +199)(x^2 -25) = 0
This has 4 complex solutions and 2 real solutions.
x^2 = 25
x = ±5
The duration required for capacity to reach 4975 units is 5 months.
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