math questions

math210finalexamfall2013.pdf

Home >Mathematics homework help >math questions

NAME: ____________________________________

Prof Marlon Seaton 12/20/2013

Berkeley College-Prof. Seaton Name: Math 210-Fall 2013 December 20, 2013 PLEASE SHOW ALL WORK WHERE POSSIBLE. PARTIAL CREDIT WILL BE GIVEN WHERE APPLICABLE

1. The wholesale price of a certain brand of bluetooth wireless headsets is given by 2( ) 30 1000P x x x , where x represents the quantity sold in units of a

thousand, that will be made available in the market by the supplier. How many units must be sold in order for the company to break-even? (8 points)

2. Bill wants to buy a car for $10,000. He makes a down payment of $2,000. He

takes out a loan to pay the remaining balance in 36 months at an interest rate of 8% compounded monthly.

(a) What will be Bill’s monthly payment? (5 points) (b) How much money will Bill actually pay at the end of 36 months? (3 points)

3. Stephen Black purchased a home for $350,000. Northridge mortgage company has approved his loan application for a 30-year fixed rate loan at 6%. He agreed to pay 25% of the purchase price as a down payment. (a) How much was the down payment amount? (2 points) (b) What was his monthly payment? (5 points)

4. John deposits $3,000 at the end of each year into an annuity paying 9% interest per year compounded semi-annually. Find the future value of this annuity after seven years. (5 points)

5. A car depreciates in linearly by a value of $1,000 per year. The original value of

the car is $30,000. Let ( )V t be the value of the car in t years. (a) Write the linear function that represents the value of the car in t years (3 points)

(b) What will be the value of the car after 5 years? (3 points)

6. Let A = 3 1 0 2

& B = 4 2 2 1

Compute: (5 points)

7. Solve the following system of equations Algebraically: (8 points)

2 7

3 4 1 x y x y

8. Let A = 1 2 4 3

B = 2 1 0 5

Find a matrix X which satisfies the following matrix equation: 2X = 2A + 3B (8 points)

9. The manufacturer of a gas clothes dryer has found that its revenue R in terms of the unit price p is given by the function: 24 4000R p p p .

(a) What unit price should the manufacturer charge to maximize revenue? (4 points)

(b) What is the maximum revenue? (3 points)

10. Perform the indicated matrix operations: (5 points)

8 3 13 6 0 4 3 13 2 1 1 2 5

13 5 22 10 1 3

11. Solve the following matrix equation below for x, y, z, and u: (6 points)

12. A company manufactures sofas and armchairs in three models A, B, and C. The company has locations in New York, New Jersey, and Chicago. In the month of August the company sends the following sofas to its location in Chicago. 10 models of A, 12 models of B, and 5 models of C. For the armchairs, they send 15 models of A, 20 models of B, and 8 models of C.

(a) Use a 2x3 matrix D to represent the above information. (3 points) (b) During the month of September, the following shipment was sent to New York. 45 model A sofas, 35 model B sofas, and 20 model C sofas. Also there were 65 model A chairs, 40 model B chairs, and 35 model C chairs. Use a 2x3 matrix E to represent the above information. (3 points)

(c) Create a 2x3 matrix F which represents the total shipment for each product for the month of August and September. (3 points)

13. A company manufactures three kinds of vitamins: Vitamin A, C, and E. Each

vitamin comes in two brands: X and Y. For brand X, they currently have the following on stock: 2 bottles of A, 7 bottles of C, and 5 bottles of E. For brand Y, they have 4 bottles of A, 6 bottles of C, and 9 bottles of E. (a) Create a 2x3 matrix A to represent the above information. (3 points) (b) The cost of brand X vitamins are: $12 for vitamin A, $18 for vitamin C, and $9

for vitamin E. The cost of brand Y vitamins are: $14 for vitamin A, $15 for vitamin C, and $10 for vitamin E. Create a 3x2 matrix B to represent this information. (3 points)