The minimum cost occurs at a production level of 3750 cups, and the cost at this level is: C(3750) = 0.00002(3750)^2(3750 + 7500) + 31 = $193.13.
The marginal cost to produce cups at a production level of x cups is given by C'(x) = 0.00006x^2 + 0.3x,
and the cost of producing 1 cup is $31. To find the cost function C(x), we need to integrate C'(x) and add the fixed cost, which is the cost of producing 1 cup.
C(x) = ∫C'(x)dx + FC Where FC is the fixed cost, which is $31.To integrate C'(x), we first find the antiderivative of the quadratic term, which is ∫0.00006x^2dx = 0.00002x^3.
To find the antiderivative of the linear term, we use the power rule, which is ∫0.3xdx = 0.15x^2. Therefore, the cost function C(x) is:C(x) = 0.00002x^3 + 0.15x^2 + 31. We can simplify this by factoring out 0.00002x^2:C(x) = 0.00002x^2(x + 7500) + 31.
The cost function C(x) is a quadratic function that increases as x increases. At x = 0, the cost is $31, which is the fixed cost. As x increases, the cost increases at a faster rate due to the quadratic term.
The minimum cost occurs at the vertex of the parabola, which is at x = -b/2a = -0.15/0.00004 = -3750.
Therefore, the minimum cost occurs at a production level of 3750 cups, and the cost at this level is:C(3750) = 0.00002(3750)^2(3750 + 7500) + 31 = $193.13.
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Describe the roots of neo-conservativism that emerged in the US
under President Ronald Reagan, who was elected in 1980.
The roots of neo-conservatism can be traced back to several key factors: Cold War and Reagan's Anti-Communism, Critique of Liberalism and Great Society Programs, Intellectual Influences, Reagan's Leadership and Communication, Foreign Policy and Defense
Cold War and Reagan's Anti-Communism: The Cold War between the United States and the Soviet Union played a crucial role in shaping neo-conservatism. Reagan, known for his strong anti-communist stance, advocated for a more assertive and confrontational approach towards the Soviet Union.
Critique of Liberalism and Great Society Programs: Neo-conservatives were critical of the liberal policies and welfare state programs of the 1960s and 1970s. They believed that these policies had led to government overreach, economic stagnation, and a decline in traditional values. They sought to roll back the growth of the state and promote free-market principles.
Intellectual Influences: The neo-conservative movement drew intellectual inspiration from thinkers such as Irving Kristol, Norman Podhoretz, and Jeane Kirkpatrick. These intellectuals questioned the dominant liberal consensus and promoted a more assertive and interventionist foreign policy, as well as a focus on traditional values and moral clarity.
Reagan's Leadership and Communication: Ronald Reagan's charismatic leadership and effective communication skills helped popularize neo-conservative ideas. His ability to articulate conservative principles in a compelling and optimistic manner resonated with many Americans, and he championed a smaller government, lower taxes, deregulation, and a strong national defense.
Foreign Policy and Defense: Neo-conservatism influenced Reagan's foreign policy, particularly in challenging Soviet expansionism and advocating for a more robust defense posture. This included supporting anti-communist movements and initiatives such as the Strategic Defense Initiative (SDI) to develop a missile defense system.
Overall, the emergence of neo-conservatism under President Ronald Reagan reflected a shift in conservative ideology towards a more assertive and interventionist approach in both domestic and foreign policy. It aimed to promote free-market principles, traditional values, and a strong defense posture, and it left a lasting impact on American politics and policy-making.
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