Let $f ( x , y ) = x ^ { 2 }$

question 8

Multiple Choice

Let $f ( x , y ) = x ^ { 2 }$ , and let $R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ . Let R be partitioned into two subrectangles by the line $x = \frac { 1 } { 2 }$ , and let $\left( x _ { i } ^ { * } , y _ { j } ^ { * } \right)$ be the center of Rij. Calculate the double Riemann sum of f.

• A) \(\frac { 3 } { 16 }\)
• B) \(\frac { 1 } { 4 }\)
• C) \(\frac { 5 } { 16 }\)
• D) \(\frac { 3 } { 8 }\)
• E) \(\frac { 7 } { 16 }\)
• F) \(\frac { 1 } { 2 }\)
• G) \(\frac { 9 } { 16 }\)

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Definitions:

Implicit Costs

Implicit costs, also known as imputed or opportunity costs, are the costs of resources owned by the firm that are used in its own production process.

Explicit Costs

Direct, out-of-pocket payments for wages, rent, materials, and other inputs in the production process.

Opportunity Costs

The value of the best alternative foregone when a decision is made to pursue a particular action, essentially the cost of choosing one option over another.

Implicit Costs

The opportunity costs of using resources owned by the firm for its own production, instead of earning income elsewhere.