Will rate a Lifesaver! Please help! Suppose that the total benefit and total cos

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Will rate a Lifesaver! Please help! Suppose that the total benefit and total cost from an activityare, respectively, given by the following equations: B(Q)= 150+28(Q)-5Q2 and C(Q) =100+8Q (Note: MB(Q) = 28 - 10Q andMC(Q) =8.) a. Write out the equation for the net benefits b. What are the net benefits when Q =1 Q=5 c. Write out the equation for the marginal net benefits d. What level of Q maximizes net benefits? Will rate a Lifesaver! Please help! Suppose that the total benefit and total cost from an activityare, respectively, given by the following equations: B(Q)= 150+28(Q)-5Q2 and C(Q) =100+8Q (Note: MB(Q) = 28 - 10Q andMC(Q) =8.) a. Write out the equation for the net benefits b. What are the net benefits when Q =1 Q=5 c. Write out the equation for the marginal net benefits d. What level of Q maximizes net benefits?

Explanation / Answer

A. Net benefits = Total Benefit - Total Costs (whichboth have equations)       Net benefits = B(Q) - C(Q)= [150 + 28Q - 5Q2] - [100 + 8Q] = 50 + 20Q-5Q2   B. Use the equation we found for net benefits (50 + 20Q- 5Q2) and plug in Q = 1 & 5    @ Q =1 NB = 50 + 20(1) -5(1)2 =65    @ Q = 5 NB = 50 + 20(5) - 5(5)2 =25 C. Solve for Net marginal benefit the same way we solvednet benefit = marginal benefit - marginal cost          = [28 -10Q] - 8 = 20 -10Q D. Net benefit is maximize when MB = MC or when netmarginal benefit (NMB) = 0       MB = MC 28 - 10Q =8, when Q = 2       NMB = 0,   0 =20 - 10Q, when Q = 2 (we expected them to be the same) So net benefit are maximized when Q = 2 B. Use the equation we found for net benefits (50 + 20Q- 5Q2) and plug in Q = 1 & 5    @ Q =1 NB = 50 + 20(1) -5(1)2 =65    @ Q = 5 NB = 50 + 20(5) - 5(5)2 =25 C. Solve for Net marginal benefit the same way we solvednet benefit = marginal benefit - marginal cost          = [28 -10Q] - 8 = 20 -10Q D. Net benefit is maximize when MB = MC or when netmarginal benefit (NMB) = 0       MB = MC 28 - 10Q =8, when Q = 2       NMB = 0,   0 =20 - 10Q, when Q = 2 (we expected them to be the same) So net benefit are maximized when Q = 2

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