Test analysis: (1) According to the unit price multiplied by the quantity, you can get the profit and get the answer.
(2) According to the properties of piecewise function, the maximum values are obtained respectively, and the answers are obtained according to the comparison of rational numbers.
(3) According to the quadratic function value greater than or equal to 4800 and the linear function value greater than or equal to 48000, the inequality is obtained, and the answer is obtained according to solving the inequality group.
Problem analysis: (1) When 1 ≤ x < 50,
When 50≤x≤90,
To sum up:
(2) When 1 ≤ x < 50, the symmetry axis of the quadratic function is x=45,
When x=45, the maximum value of y =-2× 452+180× 45+2000 = 6050,
When 50≤x≤90, y decreases with the increase of x,
When x=50, the maximum value of y =6000,
To sum up, on the 45th day, the sales profit of this commodity was the largest, with the highest profit of 6050 yuan.
(3) When 20 ≤ x ≤ 60, namely * * * 41day, the daily sales profit shall not be less than 4,800 yuan.