Question

A pottery can make B bowls and P plates in a week according to the relation:

B + P2 - 14P = 3
What is the maximum number of bowls that it can produce in a week?

Answer 1

The maximum number of bowls that can be produced in a week is approximately 43.

Step-by-step explanation:

To find the maximum number of bowls that can be produced in a week, we need to solve the given equation: B + P^2 - 14P = 3. Since we want to maximize the number of bowls (B), we need to find the highest value that satisfies this equation. By rearranging the equation and completing the square for the P terms, we get (P - 7)^2 - 49 = 3 + 49. Simplifying further, we have (P - 7)^2 = 52. Taking the square root of both sides, we get P - 7 = ±√52. Solving for P, we have P ≈ 10.576 or P ≈ 3.424. Since we can't have a fractional number of plates, we take the integer value of P, which is 10.

Substituting this value of P back into the equation, we can find the value of B. B + (10)^2 - 14(10) = 3. Simplifying further, we have B + 100 - 140 = 3. Combining like terms, we get B - 40 = 3. Solving for B, we have B ≈ 43.

Therefore, the maximum number of bowls that can be produced in a week is approximately 43.