The marketing research department for a computer company used a large city to test market their new product. They found that the relationship between the price p (in dollars) and the demand a (in number of items) was given by p = 1149 – 0.13z?.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Can you help me answer questions (A) through (C)?
![The marketing research department for a computer company used a large city to test market their new product. They found that the relationship between the price \( p \) (in dollars) and the demand \( x \) (in number of items) was given by
\[ p = 1149 - 0.13x^2. \]
1. **Find \( R(x) \), the revenue function.**
\[
R(x) = \_\_\_\_\_\_\_\_
\]
2. **(A) Find the domain of \( R(x) \).**
- **Domain:** \_\_\_\_\_\_\_\_
- **(A) Find the \( x \)-values of all local maxima of \( R(x) \).** Separate your answers by a comma. If there are none, enter NONE.
- \( x \)-values: \_\_\_\_\_\_\_\_
3. **(B) Find the \( x \)-values of all local minima of \( R(x) \).** Separate your answers by a comma. If there are none, enter NONE.
- \( x \)-values: \_\_\_\_\_\_\_\_
4. **(C) Use interval notation to indicate where \( R(x) \) is concave down.**
- Concave down: \_\_\_\_\_\_\_\_
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