Let $x=f(p,q)$ be the demand function for olive oil, and $y=g(p,q)$ be the demand function for vegetable oil, where $p$ is the price for $1$ unit of olive oil and q is the price for $1$ unit of vegetable oil. The demand functions for the two products are given such that the demand for either depends on the price for both. If a decrease in demand for one product results in an increase in demand for another product, the two products are said to be competitive, or substitute, products. If a decrease in demand for one product results in a decrease in demand for another product, the two products are complementary products. Partial derivatives can be used to test whether two products are competitive, complementary, or neither. Use the test given in the table to the right to determine the relationship between olive oil and vegetable oil.

$x=f(p,q)=7000-0\mathrm{.}04p^2+0\mathrm{.}02q^2$

$y=g(p,q)=15,000+0\mathrm{.}09p^2-0\mathrm{.}06q^2$

Test for Competitive and

Complementary Products

$\backslash$table$[[$Partial Derivatives,$\backslash$table$[[$Products A$],[$and B$]]],[f_q(p,q)>0$ and,Competitive$],[g_p(p,q)>0,($substitute$)],[f_q(p,q)<mn\; id="EditorElement\_3136428">0</mn>$ and,Complementary$],[f_q(p,q)0$ and $g_p(p,q)0,$Neither$],[f_q(p,q)0$ and $g_p(p,q)0,$Neither$]]$

Which of the following describes the relationship between olive oil and vegetable oil?

A$.$ The two products are competitive.

B$.$ The two products are complementary.

C$.$ The two products are neither competitive nor complementary.