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?"
A. 48 bowls
B. 50 bowls
C. 52 bowls
D. 54 bowls

Answer 1

To find the maximum number of bowls that a pottery can produce in a week given the relation B + P² - 14P = 3, solve for B in terms of P and calculate the maximum value by taking the derivative with respect to P and setting it equal to zero. The solution reveals that the maximum number of bowls is 52.

Step-by-step explanation:

The question asks for the maximum number of bowls a pottery can make in a week given the relation B + P² - 14P = 3. This appears to be an optimization problem typically found in algebra or precalculus. To find the maximum number of bowls, which is represented by B in the equation, we can consider the equation to be a function of P (the number of plates) and maximize it with respect to P.

First, rearrange the equation to solve for B:

B = 3 + 14P - P²

Now, treat B as a function of P: B(P) = 3 + 14P - P². To find its maximum, take the derivative with respect to P and set it equal to zero:

B'(P) = 14 - 2P

Setting the derivative equal to zero gives:

14 - 2P = 0 => P = 7

Now, substitute P = 7 back into the equation for B to find the maximum number of bowls:

B(7) = 3 + 14(7) - 7² = 3 + 98 - 49 = 52

Thus, the maximum number of bowls that can be produced in a week is 52 bowls.