Exam 2 Review

MAT 135

For exam 1 you should be able to:

  1. Solve systems of linear equations with 2 or 3 variables
  2. Add, subtract, and multiply matrices
  3. Apply matrix multiplication to business problems.
  4. Graph linear inequalities and systems of linear inequalities
  5. Solve two variable linear programming problems

Practice problems.

1. / 2. / 3.
4. / 5. / 6.

7.The next math test will contain 50 questions. Some will be worth three points while the rest will be worth six points. If the test is worth 195 points, how many three-point questions are there, and how many six-point questions are there?

Consider the following matrices.

Calculate the following values. Use your calculator wisely.

8.A + C / 9.5D
10.AX / 11. DC

12. a. A company makes 30 desks and 40 tables each day. Write this as a row vector (1x2 matrix).

b. Each desk requires 10 bolts and 5 screws. Each table requires 12 bolts and 8 screws. Write this information as a 2X2 matrix.

c. Use matrix multiplication to determine how many bolts and screws the company needs each day. Write your answer as a 2-component row vector (1X2 matrix).

d. If each bolt costs $1.00 and each screw costs 50 cents (.50), write this as a cost per unit column vector (2X1) matrix.

e. Use matrix multiplication to determine the company’s total cost of the nuts and screws each day.

13.Write a system of inequalities that when graphed will produce this region.

For each system of inequalities below, graph the system, and find the area of the shaded region if possible. (Problem 7-73)

14. / 15.

16.Sam and Emma are plant managers for the Sticky Chewy Candy Company that specializes in delectable gourmet candies. Their two most popular candies are Chocolate Chews and Peanut and Jelly Jimmies. Each batch of Chocolate Chews takes 1 teaspoon of vanilla while each batch of the Peanut and Jelly Jimmies uses two teaspoons of vanilla. They have at most 20 teaspoons of vanilla on hand as they use only the freshest of ingredients. The Chocolate Chews use two teaspoons of baking soda while the Peanut and Jelly Jimmies use three teaspoons of baking soda. They only have 36 teaspoons of baking soda on hand. Because of production restrictions, they can make no more than 15 batches of Chocolate Chews and no more than 7 batches of Peanut and Jelly Jimmies. Sam and Emma have been given the task of determining how many batches of each candy they should produce if they make $3.00 profit for each batch of Chocolate Chews and $2.00 for each batch of Peanut and Jelly Jimmies. How can they maximize their profit?

a.Define variablesd.Write the expression to be maximized or minimized

b.Set up the constraintse.Test the vertices

Test point / Value

c.Graph the system of inequalitiesf.Answer the question

and label the vertices

Solve the following systems of linear equations.

17.

18.

19.

20.Pizza Planet sells three sizes of combination pizzas.

Small (8" diameter)$8.50

Medium (10" diameter)$11.50

Large (13" diameter)$17.50

Assume that the price of the pizza can be modeled with a quadratic function, with the price dependent on the diameter of the pizza. Use the information to write three data points, and determine an equation representing the data points. If Pizza Planet is considering selling an Extra Large combination pizza, with an 18" diameter, what should such a pizza cost? If they wanted to sell a combination pizza for $50.00, how big would it have to be to fit with the rest of the price data for the pizzas?

21.Which of the following inequalities matches this graph?