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!!!
