Use a Graphing Calculator and the Method of Matrix Inverses

question 358

Multiple Choice

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
-A bookstore is having a sale. All books included in the sale have a colored sticker on them to indicate the sale price. There are green stickers, red stickers, and orange stickers. Bob, Sue, and Fred each make purchases of books that are on sale. Each row of the table gives information about the numbers of book purchases and the total cost of the purchase (before taxes) .
$\begin{array}{c|c|c|c|r}\text { Person } & \text { Green } & \text { Red } & \text { Orange } & \text { Total Cost } \\\hline \text { Bob } & 1 & 2 & 2 & \$ 28.98 \\\text { Sue } & 1 & 3 & 2 & \$ 35.85 \\\text { Fred } & 1 & 2 & 3 & \$ 34.12\end{array}$

Use this information to set up a matrix equation of the form $A X = B$ , which can be solved to determ: the price for each type of sale book. Solve this matrix equation to find the price of a book with a gree sticker.
Use the fact that for $A = \left[ \begin{array} { l l l } 1 & 2 & 2 \\ 1 & 3 & 2 \\ 1 & 2 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r r } 5 & - 2 & - 2 \\ - 1 & 1 & 0 \\ - 1 & 0 & 1 \end{array} \right]$ .

• A) \(\$ 4.96\)
• B) \(\$ 4.91\)
• C) \(\$ 4.99\)
• D) \(\$ 4.89\)

---

Definitions:

Linear Programming

A mathematical technique used to achieve the best outcome (such as maximum profit or minimum cost) in a mathematical model whose requirements are represented by linear relationships.

Subcontracting

The practice of assigning or outsourcing parts of the contractual work to third parties, often to leverage specialized skills or achieve cost efficiencies.

Inventory

The goods or materials a business holds for the ultimate goal of resale or production.

Aggregate Planner

A tool or process used to determine the optimum levels of production, inventory, and workforce required to meet forecasted demand while minimizing costs.