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3 years ago

Nequality

Mathematics

1 answer:

Slav-nsk [51]3 years ago

8 0

Answer:

The minimum number of widgets for the company to earn more than 50 dollars = 104 widgets.

Step-by-step explanation:

Complete Question

Inequality

Imagine the polynomial function shown represents the profits, in y dollars, earned by the production of x widgets.

y = -0.04x² + 40x - 3600

What is the minimum number of widgets for the company to earn more than 50 dollars?

Solution

For the profit to be more than 50

y > 50

-0.04x² + 40x - 3600 > 50

-0.04x² + 40x - 3650 > 0

0.04x² - 40x + 3650 < 0

(x - 898.4) (x - 101.6) < 0

Using the inequality table to obtain the required solution to this inequality

Eqn | x < 101.6 | 101.6 < x < 898.4 | x > 898.4

(x - 898.4) | -ve | - ve | + ve

(x - 101.6) | -ve | + ve | + ve

(x-898.4)(x-101.6) | +ve | - ve | +ve

Hence, the inequality that satisfies the equation of (x - 898.4) (x - 101.6) < 0, that is, negative, is 101.6 < x < 898.4.

And from this range, the minimum number of widgets for the company to earn more than 50 dollars = 102 widgets.

But 102 widgets give a profit of 13 dollars, 103 widgets give a profit of 47 dollars and it is until 104 widgets that the profits exceed 50 dollars truly.

Hope this Helps!!!

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