C=100+Q2,if the price of watches is birr 60,how many watches should you produce to maximize profit?
To find the number of watches that should be produced to maximize profit, we need to maximize the profit equation, which is given by P(Q) = R(Q) - C(Q), where P(Q) is the profit at a given quantity of watches Q, R(Q) is the revenue, and C(Q) is the cost.
The revenue equation, R(Q), is given by multiplying the price of the watches by the quantity: R(Q) = P x Q.
Given that the price of watches is birr 60, we can substitute this value into the revenue equation: R(Q) = 60Q.
The cost equation, C(Q), is given by the formula C = 100 + Q^2. Again, we substitute the given value for C into the equation: C(Q) = 100 + Q^2.
Now, we can substitute the revenue and cost equations into the profit equation to get: P(Q) = R(Q) - C(Q) = 60Q - (100 + Q^2).
To maximize profit, we need to find the value of Q that maximizes the profit function. We can do this by taking the derivative of the profit function with respect to Q and setting it equal to zero.
dP(Q)/dQ = 60 - 2Q = 0.
Solving for Q gives us: Q = 30.
Therefore, to maximize profit, you should produce 30 watches.