Suppose the total benefit derived from a given decision, Q, is B(Q)=25Q-Q^2 and

Question

Suppose the total benefit derived from a given decision, Q, is B(Q)=25Q-Q^2 and the corresponding total cost is C(Q) = 5 + Q^2, so that MB(Q) = 25 -2Q and MC(Q) = 2Q
What is the total cost when Q=2 and when Q=10
What is the marginal cost when Q=2 and q=10
What level of Q minimizes total cost?
What level of Q maximizes net benefits?

I need help double-checking my homework please help if you can. This is all one problem, there are two parts to the problem but this is one problem. Please also show how you arrived at the answer and everything

Explanation / Answer

a) To get total cost, substitute the qiven values of Q.
So,
C(2) = 5 + 2^2
= 9 units

C(10) = 5 + 10^2
= 105 units

b) Do the same for marginal cost
MC(2) = 2*2
= 4

MC(10) = 2*10
= 20

c) To get minimum total cost, set the marginal cost equals zero
So,
2Q = 0
Q = 0
Therefore, a value of Q = 0 minimizes the total cost

d) Likewise for maximum total benefit

25 - 2Q = 0
2Q = 25
Q = 25/2
= 12.5
A value of Q = 12.5 maximizes the total benefit.

Goodluck!

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