Suppose that the total benefit and total cost from a continuous activity are, respectively, given by the following equations: b(q) = 100 + 36q – 4q2 and c(q) =80 + 12q. (note: mb(q) = 36 – 8q and mc(q) = ) write out the equation for the net benefits.(b) what are the net benefits when q=1 and q=5? (c) write out the equation for the marginal net benefits.

A. Net benefits equation 20 + 24q - 4q^2

B. Q(1) = 40 ; Q(5) = 40

C. BE' = 24 - 8q

Explanation:

A. Net benefits:

Benefits equation - Cost equation

[100 + 36q - 4q^2] - [80 + 12q]

100 + 36q - 4q^2 - 80 - 12q

20 + 24q - 4q^2

B. replace Q=1 and Q=5

Q(1) = 20 + 24(1) - 4(1)^2

Q(1)= 44 - 4

Q(1) = 4

Q(5) = 20 + 24(5) - 4(5^2)

Q(5)= 20 + 120 - 4(25)

Q(5) = 140 - 100

Q(5) = 40

C. Marginal Benefits. First derivative of the equation wrote in section A.

Benefits equation : 20 + 24q - 4q^2

BE' = 24 - 8q

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