Determine the decision variables

Formulate the optimization model with all the constraints

• Coding in R, find the optimal number of advertisements to run in each media that maximize the expected number of exposures while satisfying all the constraints.

o What is the optimal profit value?

o What are the optimal values for the variables?

Part 2 Questions:

Using your results from Part I, formulate the total profit (as defined by Vijay).

• Use R (or any other language) to determine the optimal number of ads to run in each medium to maximize the total profit while satisfying all the constraints in Part I.

o What is the optimal profit value?

o What are the optimal values for the variables?

o Based on your calculation, what can you conclude about the accuracy of Vjay’s approximation in Part I (i.e., finding the optimal variables by using the expected number of exposures)?

Part 3 Questions:

Formulate the profit function for Vijay’s ordering problem.

• What is the decision variable?

• Determine the optimal number of gallons of Amour du jour for which Amber must order raw materials each week to maximize the restaurant’s profit. What is the optimal profit?

Sample Solution

he use of prerogative powers under the direction of the executive is a contentious subject that has been long faced by both historical and contemporary political theorists. Allowing for the exercise of extra-legal powers set within John Locke’s Second Treatise of Government’s (1689) account of political authority, Lockean prerogative theory aims to set forward the boundaries for the scope of prerogative and the ability for the successful and appropriate application of such powers during contingency and necessity. Locke’s description of prerogative is embedded in an account of political legitimacy according to the separation of powers doctrine; the legislature in a parliamentary system is considered an independent and coequal branch of government along with the executive. Despite this however, one may construe a significant power imbalance between the single-agent executive and the legislative, as a result of the large scope for prerogative imbued upon the executive which may go unchecked. John Locke’s theory and understanding of the intricate relationship between executive powers relative to that of the legislature are critical to his theory regarding the scope of administrative prerogative, specifically concerning the complex politics of resistance. John Locke describes prerogative as the ‘power to act according to discretion, for the public good, without the prescription of the law, and sometimes even against it’; therefore stating that the executive is capable of taking actions that lie beyond the given legal framework of the constitution or written laws, in the case that their actions may advance the common good of the people, and of society as a whole. Ensuring their use for the advancement of the common good of the people and the understanding that prerogative powers are not imbued as a natural right, Locke emphasises that these powers are accompanied by the right to resist unlawful government by the people. It is for this reason that for many theorists, Locke is viewed more critically as the ‘origin of our contemporary tangle of lawless emergency governance’. Locke’s theory allows for governments, and executive bodies to step outside of the law in order to deal with public concern or emergency; “where the legislative and executive power are in distinct hands, (as they are in all moderated monarchies, and well-framed governments) there the good of the society requires that several things should be left to the discretion of him that has the executive power”; therefore one may show an understanding of prerogative as a liminal concept: occupying an “in-between” space for the legislature and the executive, it is this liminality that e>

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