A furniture manufacturer produces four styles of chairs and has orders for 1000 of style A, 4000 of style B, 2000 of style C, and 1000 of style D. The following table lists the numbers of units of raw materials the manufacturer needs for each style. Suppose wood costs $5 per unit, nylon costs $3 per unit, velvet costs $4 per unit, and springs cost $4 per unit.

(a) Form a 1 × 4 matrix containing the number of units of each style ordered.
(b) Use matrix multiplication to determine the total number of units of each raw material needed.
(c) Write a 4 × 1 matrix representing the costs of the raw materials.
(d) Use matrix multiplication to find the 1 × 1 matrix that represents the total investment to fill the orders.
(e) Use matrix multiplication to determine the cost of materials for each style of chair.

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Wood Nylon Velvet Springs Style A Style B Style C Style D 10 5 5 20 10 5 20 10 5 10 10 10