Find the Absolute Minimum Value of the Function $f ( x , y ) = 6 + 3 x y - 2 x - 4 y$

question 126

Multiple Choice

Find the absolute minimum value of the function $f ( x , y ) = 6 + 3 x y - 2 x - 4 y$ on the set D. D is the region bounded by the parabola $y = x ^ { 2 }$ and the line $y = 4$

• A) \(- 31\)
• B) \(- 32\)
• C) \(- 30\)
• D) 30
• E) 0

---

Definitions:

Optimal Short-Run Output

The level of production that maximizes profit or minimizes loss in the short term.

Market Price

The current price at which an asset or service can be bought or sold, determined by the supply and demand dynamics in the market.

Downward-Sloping Demand Curves

A graphical representation indicating that as the price of a good or service decreases, the quantity demanded increases, and vice versa.

Perfect Competition

A market structure characterized by a large number of small firms, identical products, and free entry and exit from the market.