Mr.Shoemacherhas$20,000toinvestintwotypesofmutualfunds,ColemanHigh-yieldFund,andColemanEquityFund.TheHigh-yieldfundgivesanannualyieldof12%,whiletheEquityfundearns8%.Mr.Shoemacherwouldliketoinvestatleast$3000intheHigh-yieldfundandatleast$4000intheEquityfund.Howmuchmoneyshouldheinvestineachtomaximizehisannualyield,andwhatisthemaximumyield?Solvethefollowingsystemoflinearequations,usingaugmentedmatrixmethods.Showfullwork.

-2x + y = -3

4x - 3y = 5

3.You are the chief financial officer for Freestate Power & Light, an energy company producing electricity for greater Megalopolis. Your electric plant runs on natural gas provided by Galactic Gas, an energy company supplying greater Megalopolis with natural gas. Galactics natural gas wells and distribution system are powered by your electricity. The following graphic shows the flow of monthly product output for each energy company (in $ millions) to its consumers and to each other.

This graphic indicates the following equations for the monthly outputs a and b:

Freestate output: a = 0.5 b + 6

Galactic output: b = 0.25 a + 2

Rewrite these equations to support augmented matrix format: get variables in the same order on the left and constants on the right.

Use this system of linear equations to solve for monthly outputs a and b using augmented matrix methods. Show your work.

4.Solve the following system of linear equations, using augmented matrix methods. Show full work.

2x 3y = 1

-6x + 9y = -3

5. Graph the inequality 3x + 2y 6 and show the solution set (use following grid, if desired)

6.Graph the system: x + y 2

2x y 2

and obtain the coordinates of the corner point in the solution region (the point that is the intersection of two boundary lines - excluding the x-axis and the y-axis).

7. Consider the following graph of a feasible region, which is bounded by the lines

3x + y = 5, 3x + y = 3, x = 0, and y = 0, as indicated.

(a) Write the system of inequalities corresponding to the graph of the feasible region

(For each , replace by either or , as appropriate and explain your reason):

3x + y 5

3x + y 3

x 0

y 0

(b) Find the coordinates of the corner points A, B, C, and D of the feasible region.

For each of the four corner points, state which system of equations must be solved, and show how to solve it.

A:

B:

C:

D: