# Question: a company manufactures 2 products a and b for 100...

###### Question details

A company manufactures 2 products: A and B. For $1.00 worth of product A, the company spends $0.45 on materials; $0.25 on labor and $0.15 on overhead. For B, the costs are $0.40, $0.30 and $0.15 respectively. If the company has Qm dollars worth of materials, Ql dollars worth of labor and Qo dollars worth of overhead, and the company plans to produce xa dollars worth of A and xb dollars worth of B. #1(i) Describe the above scenario using a linear system in terms of xa, xb. Here Qm, Ql , Qo are positive constants. #1(ii) Reduce the augmented matrix of the system in the previous part to a reduced echelon system. In order for the system to have at least one solution, what condition(s) do Qm, Ql , Qo need to satisfy? #1(iii) If the system has at least one solution, solve for xa, xb in terms of Qm, Ql , Qo.