If you have never done this before - go to CASA for fingerprint/picture process before your test date.

Transcription

1 MATH 33 Review for Test - When: Where: CASA Testing Center Time: minutes Number of questions: 3 Multiple Choice Questions (total: 84 points) Free Response Questions (total: 6 points) For the free response part, please show your work neatly, do not skip steps. What is covered: Sections.4 and.; Chapters and 3. Do not forget to reserve a seat for Test. If you have never done this before - go to CASA for fingerprint/picture process before your test date. Take practice Test! % of your best score will be added to your test grade. When you take the test, you will see a score in your CASA grade sheet right away. That score is for the multiple choice part only. So, it is out of 84 points. The grade for the Free Response Part will be posted later, after the papers are graded. Do not be late for your test. Plan to be at the testing center - minutes before your scheduled time. If you miss your scheduled time; log in to your CASA account and try to reschedule - you can reschedule if there are any available seats. You can NOT bring a calculator with you. There will be a calculator available on the computer, you can use that one. It is the same calculator that is available on your CASA account. Practicing with that calculator may be helpful to save time in the test. When you log in to your casa account and click on 33, there is a link that says calculator, click on it and do some computations (when you re taking your practice test for example). Remember the make up policy: NO MAKE UPS! If you miss the test, you will get. The final will replace ONE missed test.

2 Example: A manufacturer has a monthly fixed cost of $4, and a production cost of $8 for each unit produced. The product sells for $6 per unit. a) The cost function for this situation is b) The revenue function for this situation is c) The profit function is d) The break even quantity is e) The break even revenue is f) What is the profit (or loss) if 7, units are produced and sold? g) How many items should be produced to make a profit of $,?

3 Example: A car is worth $,. when purchased. It is depreciated linearly over years and has a scrap value of $,.. A linear equation expressing the car's book value at the end of t years is What is the value of the car after 3 years? 3

4 Example: Are the following matrices in row-reduced form? 4

5 Example: Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Solve the system. a) b) 4 c) d) 4

6 6 Example: Solve the system for u: Exercise: Solve the same system for y and z u y z u y

7 Example: Solve the following system using Gauss-Jordan elimination method. x y 4z y z 3 4y z 6 7

8 Example: Solve the system of equations by using the inverse of the coefficient matrix. x y 4x 6y 44 8

9 Example: Give the optimal solution (point and value). Maximize C = x + 4y Subject to x+4y < x + y 6 x y 9

10 Example: A nutritionist at the Medical Center has been asked to prepare a special diet that will supplement a patient s diet by adding at least 86 mg of Vitamin B and at least 68 mg of Vitamin D per day. He can get the desired amount of vitamins from two brands of vitamins Brand I and Brand II. Each pill of Brand I contains mg of Vitamin B and mg of Vitamin D. Each pill of Brand II contains 8 mg of Vitamin B and 9 mg of Vitamin D. Each pill of Brand I costs $. and each pill of Brand II costs $.. Suppose you want to know how many pills per day of each brand should be prescribed to minimize cost. Let x = the number of pills of Brand I and y = the number of pills of Brand II. What would be an appropriate objective function? What are the constraints?

11 Example: B, What is the inverse of B? 4 Example: Given: D. 6 What is the transpose of matrix D?

12 EXERCISE solve these for practice. Given B, C, and D What are the dimensions of B, C and D? What is the determinant of B? What is the inverse of B? What is the transpose of C? 4 D C + D = B D B C D B C D T