1. EXAMPLE 3 Solve a multi-step problem Manufacturing A company manufactures small and large steel DVD racks with wooden bases. Each size of rack is available in three types of wood: walnut, pine, and cherry. Sales of the racks for last month and this month are shown below.

2. EXAMPLE 3 Organize the data using two matrices, one for last month’s sales and one for this month’s sales. Then write and interpret a matrix giving the average monthly sales for the two month period. SOLUTION STEP 1 Organize the data using two 3 X 2 matrices, as shown. Solve a multi-step problem Walnut Pine Cherry 125 100 278 251 225 270 95 114 316 215 205 300 Last Month (A) This Month (B) Small Large

3. EXAMPLE 3 Solve a multi-step problem 220 214 594 466 430 570 1 2 = (A + B) = 1 2 1 2 125 100 278 251 225 270 95 114 316 215 205 300 + STEP 2 Write a matrix for the average monthly sales by first adding A and B to find the total sales and then multiplying the result by. 1 2

4. EXAMPLE 3 Solve a multi-step problem 110 107 297 233 215 285 = STEP 3 Interpret the matrix from Step 2. The company sold an average of 110 small walnut racks, 107 large walnut racks, 297 small pine racks, 233 large pine racks, 215 small cherry racks, and 285 large cherry racks.

5. EXAMPLE 4 Solve a matrix equation SOLUTION Simplify the left side of the equation. Write original equation. Solve the matrix equation for x and y. 5x –2 6 –4 3 7 –5 –y –21 15 3 –24 =+ 3 5x –2 6 –4 3 7 –5 –y –21 15 3 –24 = 3 +

6. EXAMPLE 4 Solve a matrix equation Add matrices inside parentheses. Perform scalar multiplication. Equate corresponding elements and solve the two resulting equations. The solution is x = –2 and y = 4. ANSWER 5x + 3 1 5 –4 – y –21 15 3 –24 = 3 15x + 9 15 3 –12 – 3y –21 15 3 –24 = –12 – 3y = 224 y = 4 15x + 9 = –21 x = –2

7. GUIDED PRACTICE for Examples 3 and 4 5. In Example 3, find B – A and explain what information this matrix gives. –30 14 38 –36 –20 30 The difference in the number of DVD racks sold this month compare last month. ANSWER

8. GUIDED PRACTICE for Examples 3 and 4 6. Solve –2 –3x –1 4 y 9 –4 –5 3 12 10 2 –18 = + for x and y. x = 5 and y = 6 ANSWER