Use the Barycentric Coordinates with Respect to S to Determine $$\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } , \right\}$$

question 6

Multiple Choice

Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.
- $$\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } , \right\}$$
Barycentric coordinates: $\left( \frac { 1 } { 2 } , 0 , \frac { 1 } { 8 } , \frac { 3 } { 8 } \right)$

• A) Inside
• B) Outside
• C) Edge
• D) Face

---

Definitions:

Preference

An economic term referring to the assumption that individuals have the capacity to order or rank different bundles of goods or outcomes in terms of their satisfaction.

Substitutes

Products or services that can be used in place of each other, where an increase in the price of one leads to an increase in demand for the other.

Market-Clearing Level

Market-Clearing Level is the price point at which the quantity of goods supplied is equal to the quantity of goods demanded, eliminating any surplus or shortage in the market.

Quantity Supplied

The total amount of a good or service that producers are willing and able to sell at a given price over a specific period.