Name _____________
Period ____
Finite
4.1 WS
Systems of Linear Equations
Graph each inequality.
1. 𝒙 ≥ 𝟎
𝒙+𝒚 ≥ 𝟐
3. { 𝒙 ≥ 𝟎
𝒚 ≥𝟎
2. 𝒚 ≥ 𝟎
𝑥+𝑦 ≥0
𝑥+𝑦 ≤8
2𝑥
+ 𝑦 ≤ 10
4.
𝑥≥0
{ 𝑦≥0
Determine which region a,b,c or do represents the graph of the given system of linear
inequalities. The regions a,b,c, and d are nonoverlapping regions bounded by the indicated
lines.
5.
7. Graph
6.
8. Mixture Problem: Nutt’s Buts has 60 pounds of almonds and 90 pounds of peanuts available. These are to be mixed in 1-pound
packages as follows: a low-grade mixture that contains 4 ounces of almonds and 12 ounces of peanuts and a high-grade mixture that contains 8
ounces of almonds and 8 ounces of peanuts.
Use x to denote the number of packages of the low-grade mix and y to denote the number of packages of the high-grade mixture. Write a system
of linear inequalities that describes the possible number of each kind of package and graph the system, listing corner points.
9. Manufactoring: Mike’s Famous Toy Trucks company manufactures two kinds of toy trucks- a dumpster and a tanker. In the
manufacturing process, each dumpster requires 3 hours of grinding and 4 hours of finishing, while each tanker requires 2 hours of grinding and 3
hours of finishing. The company has two grinders and three finishers, each of whom works at most 40 hours per week.
Use x to denote the number of dumpsters and y to denote the number of tankers. Write a system of linear equations that describes the possible
numbers of each truck that can be manufactured per week. Graph the system and list any corner points.
10. Financial Planning: The Harpers have up to $25,000 to invest. As their financial advisor, you recommend they make the
following investments in two funds based on their average yearly performance for the past 5 years ending Dec 31, 2009: at least
$15,000 in a Dividend Equity fund with an average yearly return of 6% and at most $10,000 in a Global Bond fund with an
average yearly return of 9%.
Use x to denote the amount invested in Dividend Equity fund and y to denote the amount to be invested in the Global Bond fund.
Write a system of inequalities that describes this situation. Graph the system and list its corner points.
11. Nutrition: A farmer prepares feed for livestock by combining two types of grain. Each unit of the first grain contains 1 unit of protein an
d5 units of iron while each unit of the second grain contains 2 units of protein and 1 unit of iron. Each animal must receive at least 5 units of
protein and 16 units of iron each day. Write a system of linear inequalities that describes the possible amounts of each grain the farmer needs to
prepare. Graph the system and list its corner points.