https://file.aiquickdraw.com/mathbot/file/17266864692543tpkze4d.jpg

To solve this problem using matrix multiplication, we need to multiply the matrix of items ordered with the vector of costs for each item.

### Step 1: Define the matrices
Let the matrix of the orders be:
\[
A = \begin{bmatrix}
3 & 5 & 4 \\
8 & 10 & 10 \\
5 & 1 & 2
\end{bmatrix}
\]
This matrix represents the number of tubs of popcorn, bags of candy, and sodas ordered for Order 1, Order 2, and Order 3, respectively.

The cost vector for the items is:
\[
B = \begin{bmatrix}
7.42 \\
4.38 \\
4.98
\end{bmatrix}
\]
This vector represents the cost of popcorn, candy, and soda.

### Step 2: Perform matrix multiplication
To find the total cost for each order, we multiply the matrix $A$ by the vector $B$:
\[
\text{Total Cost} = A \times B
\]

I'll now compute this multiplication.The total cost for each order is as follows:

- **Order 1**: \$64.08
- **Order 2**: \$152.96
- **Order 3**: \$51.44

These totals were found using matrix multiplication.

Would you like more details on how the matrix multiplication was performed, or do you have any other questions?

Here are 5 related questions:
1. How is matrix multiplication applied in other real-world scenarios?
2. What are the rules for matrix multiplication?
3. How does matrix multiplication differ from element-wise multiplication?
4. How can we apply linear algebra techniques to optimize pricing strategies?
5. How would the total change if we modified the costs of one of the items?

**Tip:** When performing matrix multiplication, ensure that the number of columns in the first matrix equals the number of rows in the second matrix to make the multiplication possible.

The number of tubs of popcorn, bags of candy, and sodas from three orders at a movie theatre are listed below along with the cost of each item. Use matrix multiplication to find the total for each order.

Learn how to use matrix multiplication to calculate the total cost of three different orders at a movie theatre, based on the number of tubs of popcorn, bags of candy, and sodas purchased. Costs of each item are multiplied with the respective order quantities to find the total using linear algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation