MSM 711

2.3 Applications of Linear Systems

1. The Upside Down Company specializes in making down jackets, ski vests and comforters. The requirements for down and labor and the profits earned are given in the accompanying chart.

	Down (lbs)	Time (labor-hours)	Profit ($)
Jacket	3	2	6
Vest	2	1	6
Comforter	4	1	2

Each week the company has available 600 pounds of down and 275 labor-hours and wants to earn a profit of $1150. How many of each item should the company make each week?

2. A 600-seat movie theater charges $5.50 admission for adults and $2.50 admission for children. If the theater is full and $1911 is collected, how many adults and how many children are in the audience?

3. A bank wishes to invest a $100,000 trust fund in three sources, bonds paying 8%, certificates of deposit paying 7% and first mortgages paying 10%. The bank wishes to realize an $8000 annual income from the investment. A condition of the trust is that the total amount invested in bonds and certificates of deposit must be triple the amount invested in mortgages. How much should the bank invest in each possible category? Let x, y, and z, respectively, be the amounts invested in bonds, certificates of deposit, and first mortgages.

4. p. 46 #27 Solve the system.

5. p. 47 # 29 Solve the system.