A firm makes chairs and tables. The units of wood, metal and paint needed for one item are given by the matrix R (row 1: chair, row 2: table; columns: wood, metal, paint). An order for 40 chairs and 25 tables is written as the row matrix Q.
\(R = \begin{bmatrix} 3 & 2 & 1 \\ 5 & 6 & 2 \end{bmatrix}\), \(Q = \begin{bmatrix} 40 & 25 \end{bmatrix}\)
Match List-I with List-II
| List-I | List-II | ||
| (A) | Total units of wood needed for the order | (I) | 230 |
| (B) | Total units of metal needed for the order | (II) | 90 |
| (C) | Total units of paint needed for the order | (III) | 150 |
| (D) | Units of metal needed for the tables alone | (IV) | 245 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
Q is of order \(1 \times 2\) and R is of order \(2 \times 3\), so QR is a \(1 \times 3\) row matrix giving the total units of wood, metal and paint. Each element is the row Q times one column of R.
(A) Total units of wood needed for the order
This matches (IV) 245.
\(40 \times 3 + 25 \times 5 = 120 + 125 = 245\)
(B) Total units of metal needed for the order
This matches (I) 230.
\(40 \times 2 + 25 \times 6 = 80 + 150 = 230\)
(C) Total units of paint needed for the order
This matches (II) 90.
\(40 \times 1 + 25 \times 2 = 40 + 50 = 90\)
(D) Units of metal needed for the tables alone
This matches (III) 150. It is only the table part of the metal total:
\(25 \times 6 = 150\)