# Evaluating Functions and Systems of Linear Equations and Inequalities

(See attached file for full problem description)

1. Graph f(x) = -2x + 2.

2. Rewrite the equation -x - 10y = 50 as a function of x.

3. Given f(x) = 5x2 - 3x + 1, find f(-2).

A) -13

B) 15

C) -25

D) 27

4. Given f(x) = 4x - 5, find f(a - 1).

A) 4a - 9

B) 4a - 6

C) a - 2

D) a - 9

5. Graph the inequality.

2x + 3y > 6

6. Are the following lines parallel, perpendicular, or neither?

L1 with equation x - 6y = 30

L2 with equation 6x + y = 6

A) Parallel

B) Perpendicular

C) Neither

7. Given g(x) = 4x - 3, find g(3a).

8. Graph the inequality.

x  2

9. Given f(x) = x2 - x + 7, find f(0).

10. Given f(x) = 4x + 4, find f(0).

1. Solve the system by addition.

5x - 3y = 13

4x - 3y = 11

2. The sum of two numbers is 90. The second is 10 more than 4 times the first. What are the two numbers?

3. Solve the system by graphing.

x + y = 4

-x + y = 2

4. Solve the following system of linear inequalities by graphing.

x - y  3

x + 2y  6

5. Solve the system by addition or substitution.

3x + 6y = 0

x =

6. Adult tickets for a play cost $17 and child tickets cost $8. If there were 24 people at a performance and the theater collected $363 from ticket sales, how many children attended the play?

A) 4 children

B) 5 children

C) 6 children

D) 19 children

7. Solve the following system of linear inequalities by graphing.

3x + 4y  12

x + 3y  6

x  0

y  0

A)

B)

C)

D)

9. Solve the system by graphing.

2x + y = 4

x + y = 3

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#### Solution Preview

Please see the attached file for details.

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Please help with the following :

(See attached file for full problem description)

1. Graph f(x) = -2x + 2.

2. Rewrite the equation -x - 10y = 50 as a function of x.

As -x - 10y = 50, we get

y= -0.1x-5

3. Given f(x) = 5x2 - 3x + 1, find f(-2).

A) -13

B) 15

C) -25

D) 27

As , (D) is the answer.

4. Given f(x) = 4x - 5, find f(a - 1).

A) 4a - 9

B) 4a - 6

C) a - 2

D) a - 9

As , (A) is the answer.

5. Graph the inequality.

2x + 3y > 6

6. Are the following lines parallel, perpendicular, or neither?

L1 with equation x - 6y = 30

L2 with equation 6x + y = 6

A) Parallel

B) Perpendicular

C) Neither

As ...

#### Solution Summary

Evaluating Functions and Systems of Linear Equations and Inequalities are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Graphical Approach for Solving Linear Programming Problems

This is liner programming problem for optimization of an objective function subject to some liner constraints. There are two profit maximization problems and two cost minimization problems.

For each problems below complete the following:

a) Graph and label every inequality. State the scale used on both axes.

b) Shade the feasible region.

c) State the coordinates of all corner points.

d) Evaluate the objective function for every corner point.

e) State the optimal value of the objective function along with the coordinates of the corner point. For the last two problems state the final answer in practical words.

1) Solve the following linear programming problems using the method of corners.

Maximize P = 3x + 2y subject to (see attached file for equations).

2) Solve the following linear programming problem using the method of corners.

Minimize C = 2x + 4y subject to (see attached file for equations)

3) K.L. Manufacturing wants to maximize its profit on products A and B. The profit on one unit of Product A is $40, while the profit on Product B is $20. Each unit of Product A requires 10 hours of assembly time and 2 hours of finishing time, while each unit of Product B requires 2 hours of assembly time and 4 hours of finishing time. The departmental capacity (in total hours) is 20,000 for assembly and 31,000 for finishing. What is the maximum profit, and how many of each product should be produced to achieve that profit? Write the objective function and system of linear inequalities and solve it graphically using the method of corners.

4) Two varieties of animal feed contain essential nutrients A and B. Feed I contains 2 units of A and 3 units of B per pound. Feed II contains 2 units of A and 5 units of B per pound. A farmer needs a feed mix that will give his animals a minimum of 16 units of A and 30 units of B. If Feed I costs $3 per pound and Feed II costs $4 per pound, how much of each should be bought to supply the proper nutrition while minimizing cost? Write the objective function and system of linear inequalities and solve it graphically using the method of corners.

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