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A furniture company produces tables, chairs and benches, and sells these separately or in sets. For a table they need 12 units wood and 3 units metal. For a bench it is 6 units wood, 2 units metal and 5 units fabric. A chair is made from 2 units wood, 1 unit metal and 2 units fabric. Two types of sets are composed: set A consists of a table and four chairs, and set B contains a table, three chairs and a bench. a) Find the production matrix M that is used to calculate the necessary amounts of wood, metal and fabric to produce x tables, y chairs and z benches. b) Find the production matrix P that is used to calculate the necessary amounts of wood, metal and fabric to produce m sets of type A and n sets of type B. c) An order is for 40 sets of type A, 60 sets of type B and 10 (extra) benches. How many units of wood, metal and fabric are needed for this order?

A furniture company produces tables, chairs and benches, and sells these separately or in sets. For a table they need 12 units wood and 3 units metal. For a bench it is 6 units wood, 2 units metal and 5 units fabric. A chair is made from 2 units wood, 1 unit metal and 2 units fabric. Two types of sets are composed: set A consists of a table and four chairs, and set B contains a table, three chairs and a bench. a) Find the production matrix M that is used to calculate the necessary amounts of wood, metal and fabric to produce x tables, y chairs and z benches. b) Find the production matrix P that is used to calculate the necessary amounts of wood, metal and fabric to produce m sets of type A and n sets of type B. c) An order is for 40 sets of type A, 60 sets of type B and 10 (extra) benches. How many units of wood, metal and fabric are needed for this order?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A furniture company produces tables, chairs and benches, and sells these separately or in sets. For a table they need 12 units wood and 3 units metal. For a bench it is 6 units wood, 2 units metal and 5 units fabric. A chair is made from 2 units wood, 1 unit metal and 2 units fabric. Two types of sets are composed: set A consists of a table and four chairs, and set B contains a table, three chairs and a bench. a) Find the production matrix M that is used to calculate the necessary amounts of wood, metal and fabric to produce x tables, y chairs and z benches. b) Find the production matrix P that is used to calculate the necessary amounts of wood, metal and fabric to produce m sets of type A and n sets of type B. c) An order is for 40 sets of type A, 60 sets of type B and 10 (extra) benches. How many units of wood, metal and fabric are needed for this order? d) If a unit of wood costs $2, a unit of metal $4, and a unit of fabric $7, how much does the furniture company pay for materials to produce the order in task c)? Note: Solve tasks c) and d) with appropriate matrix products.
Transcribed Image Text:A furniture company produces tables, chairs and benches, and sells these separately or in sets. For a table they need 12 units wood and 3 units metal. For a bench it is 6 units wood, 2 units metal and 5 units fabric. A chair is made from 2 units wood, 1 unit metal and 2 units fabric. Two types of sets are composed: set A consists of a table and four chairs, and set B contains a table, three chairs and a bench. a) Find the production matrix M that is used to calculate the necessary amounts of wood, metal and fabric to produce x tables, y chairs and z benches. b) Find the production matrix P that is used to calculate the necessary amounts of wood, metal and fabric to produce m sets of type A and n sets of type B. c) An order is for 40 sets of type A, 60 sets of type B and 10 (extra) benches. How many units of wood, metal and fabric are needed for this order? d) If a unit of wood costs $2, a unit of metal $4, and a unit of fabric $7, how much does the furniture company pay for materials to produce the order in task c)? Note: Solve tasks c) and d) with appropriate matrix products.
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