Suppose total benefits and total costs are given by B(Y)= 100Y − 8Y² and C(Y)= 10Y².What is the maximum level of net benefits (rounded to the nearest whole number)? A) 92 B) 139 C) 78 D) None of the statements associated with this question are correct.

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Quizplus · Accepted Answer

Net benefits are calculated as the difference between total benefits and total costs. Given B(Y) = 100Y - 8Y^2 and C(Y) = 10Y^2, net benefits (NB) can be expressed as NB(Y) = B(Y) - C(Y) = 100Y - 8Y^2 - 10Y^2 = 100Y - 18Y^2. To find the maximum level of net benefits, we need to find the derivative of NB(Y) with respect to Y, set it to zero, and solve for Y. The derivative of NB(Y) with respect to Y is dNB/dY = 100 - 36Y. Setting this equal to zero gives 100 - 36Y = 0, which implies Y = 100/36 = 2.78. Substituting Y = 2.78 back into the net benefits equation gives NB(2.78) ≈ 100(2.78) - 18(2.78)^2 ≈ 139 (rounded to the nearest whole number).

Suppose Total Benefits and Total Costs Are Given by B(Y)=