Practice Exam #2 Math 1160 The material on this exam does not cover all of the possible topics that could be on the real exam. This practice exam is meant as supplement to the normal studying routines before exams. It is imperative that you look over all course materials and do not rely on the practice exam to “give you the problems”. Other materials you should study: Quizzes Homework Notes from lecture and discussion Practice Exam Supply and Demand problems! To be successful on a math test you must start studying early. Waiting until the night before is usually a recipe for disaster! Leave yourself time to ask questions, stay rested, and relax! 1 | P a g e 1.) You are in charge of purchases at the student run bookstore at your college and you must decided how many calculus, history, and marketing books you must purchase from students for resale. Due to budget restrictions, you cannot purchase more than 650 books each semester. There are also shelf limitations: Calculus books take up 2 inches of space, History books take up 1 inch of space, and Market books take up 3 inches of space. The student run book store only has 1000 inches of shelf space available. If the used book program makes a $10 profit of each Calculus book, $4 per History book, and $8 on each Marketing book, how many of each type should you purchase? SET UP THE PROBLEM. DO NOT SOLVE. Decision Variables (with description): Objective Function: Subject to constraints: 2 | P a g e 2.) Use the following graph and matching system of linear inequalities to answer the following questions. Objective function Subject to P = 20 x1 + 10 x 2
x1 + 2 x 2 ≤ 24
x1 + x 2 ≤ 18
x1 , x 2 ≥ 0
a). On the graph area provided, indicate the solution region. x2
30
20
10
x1
10
20
30
b). Determine all the corner points associated with the region. c). 3 | P a g e Maximize and minimize P = 20 x1 + 10 x 2 subject to the constraints provided. 3.) Solve the following maximization problem using the graphical method. P = 10 x + 2 y
2x + 2 y ≤ 4
−x + y ≤ 1
x, y ≥ 0
4.) Solve the following system of equations using the graphical method and state whether the feasible region is bounded or unbounded: Minimize C = 3x1 + x 2 10 x1 + 2 x 2 ≥ 84
Subject to: 8 x1 + 4 x 2 ≥ 120 x1 , x 2 ≥ 0
4 | P a g e 5.) Solve for x: 3 log b 2 +
1
log b 25 − log b 20 = log b x
2
6.) Solve for x: Solve for x: 3 x 2 + 12 x + 6 = 0 7.) Use the following f ( x) = −4 x 2 + 16 x − 15 to answer the following: b.) Indicate the vertex c.) Find the maximum or minimum, explain d.) Find the axis of symmetry e.) Find the x and y intercepts f.) Graph the function labeling all of the above (intercepts, y, x, axis of symmetry, vertex, max or min) 5 | P a g e 8.) Solve the following equations for x. a.) 10 2 x −3 = 10 x +10 b.) ( x + 2) 3 = 10 3 c.) 2 x + 2 = 4 3 x 9.) Suppose that $2,500 is invested at 8% compounded quarterly. How much money will be in the account after a.) 6 months? b.) 2 years? c.) 20 years? 10.) Solve the following logarithmic function 3
2
log b 4 − log b 8 + log b 2 = log b x 2
3
11.) Rewrite the following function in logarithmic notation x = 10 y 6 | P a g e 12.) $3,000 is invested for 2 years at 3% per year. Compute the simple interest for the specified period and the future value at the end of the period. (Round all answers to the nearest cent.) 13.) An investment earns 6% per year and is worth $60,000 after 2 years. Find the present value of the investment using simple interest. (Round your answer to the nearest cent.) 14.) Calculate, to the nearest cent, the future value of an investment of $10,000 at 3.5%/year compounded quarterly (4 times/year) after 5 years. 15.) Find the effective annual interest rate of 2% compounded monthly. Round your answer to the nearest 0.01%. 16.) You deposit monthly $1000 in an account at the Lifelong Trust Savings and Loan that pays 4% interest compounded quarterly. By how much will your deposit have grown after 6 years? 7 | P a g e 17.) The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q = −2.5p + 800, where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? What is the largest monthly revenue? 18.) How much do you need to save per week in order to reach a retirement goal of 3 million dollars in 35 years if you are certain you can get 8% interest? 19.) How long will a saving of 1 million dollars last you if you withdraw $15,000 per month and your savings account accrues 4% interest? 8 | P a g e