Arnie Ziffel Has $20 Per Week to Spend on Any

question 141

Essay

Arnie Ziffel has $20 per week to spend on any combination of pineapples and green tea.The price of a pineapple is $4 and the price of a bottle of green tea is $2.The table below shows Arnie's utility values.Use the table to answer the questions that follow the table.
$\begin{array}{|c|c|l|l|l|l|l|l|}\hline\text { Quantity }& & & \text { Marginal } & \text { Quantity }&\text { } &&\text { Marginal } \\\text { of }&\text { Total } & \text { Marginal } & \text { Utility per }&\text { of Green } & \text { Total }&\text {Marginal } &\text { Utility per } \\\text { Pineapples } & \text { Utility } & \text { Utility } & \text { Dollar } & \text { Tea } & \text { Utility } & \text { Utility } & \text { Dollar } \\\hline 1 & 32 & & & 1 & 28 & & \\\hline 2 & 52 & & & 2 & 46 & & \\\hline 3 & 64 & & & 3 & 54 & & \\\hline 4 & 68 & & & 4 & 60 & & \\\hline 5 & 70 & & & 5 & 64 & & \\\hline 6 & 71 & & & 6 & 66 & & \\\hline 7 & 71 & & & 7 & 67 & & \\\hline\end{array}$
a.Complete the table by filling in the blank spaces.
b.Suppose Arnold purchases 4 pineapples and 2 bottles of green tea.Is he consuming the optimal consumption bundle? If so,explain why.If not,what combination should he buy and why?

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Definitions:

Dual Value

The concept in linear programming and optimization that assigns a value to the constraints, reflecting their contribution to the objective function when slightly relaxed.

Iso-Profit Line

A graphical representation in economic models showing combinations of inputs that yield the same level of profit.

Graphical Maximization

A technique used in operations research and economics to find the highest value of an objective function given certain constraints, represented graphically.

Feasible Region

In optimization problems, the set of all possible points that satisfy the problem's constraints and are therefore considered for the solution.