Question

A manufacturing company plans to progressively increase its production capacity over the next few quarters. (A quarter is a period 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?

Answer 1

5 months

Explanation:

We assume that y represents production capacity, rather than increase 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.