**Solution: ** Let the number of articles produced in a day = x

∴ Cost of production of each article = Z (2x + 3)

According to the condition,

Total cost = 90

⇒ x × (2x + 3) = 90

⇒ 2x^{2} + 3x = 90

⇒ 2x^{2} + 3x – 90 = 0

⇒ 2x^{2 }– 12x + 15x – 90 = 0

⇒ 2x(x – 6) + 15(x – 6) = 0

⇒ (x – 6) (2x+15) = 0

⇒ x – 6 = 0 ⇒ x = 6

But the number of articles cannot be negative.

⇒ x = 6

∴ Cost of each article = Rs (2 × 6 + 3) = Rs. 15

Thus, the required number of articles produced is 6 and the cost of each article is Rs. 15.