Question

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing

Answer 1

If Wilson produces only one 1 bag, then his profit starts decreasing

How to determine the point

Given the function;

Let  f ( x ) = $2x^4 - 4x^3 + 7$

Where;

x is  the number of bags of cereal produced

$f'x = 2x^4 - 4x^3 + 7$

$f'(x) = 8x^3 - 12x^2$

Factorize the expression

$f'(x) = 4x^2(2x - 3)$

If the value of x is decreasing, we have;

f ′ ( x ) ≤ 0

4x² (2x - 3) ≤ 0

If x² ≥ 0, then;

2x - 3  ≤ 0

x ≤ 3/ 2

With x as the number of bags

x ∈ N

x = 1 is the only possibility

Thus, if Wilson produces only one 1 bag, then his profit starts decreasing

Learn more about functions here:

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The complete question:

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: pi = 2x ^ 4 - 4x ^ 3 + 7,  where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing