Exam 1



EXAM 1

MATH 141 Business Mathematics I

Fall 2006 Version A

Nite

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• You have 75 minutes to complete the exam.

• You must show appropriate, legible work to receive credit. Include all intermediate steps and functions you use on your calculator.

• Check to make sure there are 5 pages, besides the cover page, when you begin the exam.

• SCHOLASTIC DISHONESTY WILL NOT BE TOLERATED.

GOOD LUCK!!

EXAM 1

(6 points)

1. Pivot about the element circled in the given matrix. Describe your process and show the intermediary steps.

[pic]

(6 points)

2. It takes [pic] of an hour and costs $2 to make one color ink cartridge, [pic] of an hour and costs $1 to make a regular black ink cartridge, and [pic] of an hour and costs $1.50 to make one super black ink cartridge. The number of black ink cartridge needed is 20% more than the number of color ink cartridges needed. If 10 hours and $40 are available, how many of each type cartridge can be made? Set up but do not solve the problem.

(6 points)

3. At an original price of $3.50, consumers will buy 500 boxes of cookies and producers will provide 250 boxes of cookies to the market. If the original price increases by 25 cents, consumers will buy 100 fewer boxes of the cookies. However, if the original price increases by 50 cents, producers will provide 300 additional boxes of the cookies.

Find the supply equation.

(12 points)

4. Circle the correct choice for each statement.

T F a. The demand equation expresses the relationship between the unit price and the amount the manufacturer decides that he will provide.

T F b. The demand equation is generally an increasing function.

T F c. The profit is found by multiplying the number of units by the price for each unit.

T F d. The supply equation is generally an increasing function.

T F e. The break-even quantity is the number of units at which the revenue is zero.

T F f. The linear depreciation equation is a decreasing function.

A survey was conducted in a particular area of the U.S. to find out how many people, on average, read a particular new magazine each month. The results are given below.

|Month |1 |2 |3 |4 |5 |

|Avg. # of Readers | | | | | |

|(in thousand) |1.28 |1.12 |1.45 |1.98 |2.06 |

(4 points)

5. Find the equation of the least-squares line for this data, describing the average number of readers as a function of the number of months the magazine has been published. Give all coefficients and constants to 3 decimal places.

(4 points)

6. Give an interpretation of the value of the slope found for the line in #6.

(4 points)

7. If this trend continues, predict when there will be an average of three thousand readers in one month.

(4 points)

8. If this trend continues, how many readers, on average, would be reading the magazine in month 30?

(6 points)

9. Solve the following system of equations: 2x - y + 3z = 3

x = 3y – 4z + 2

-y + 10z + 5x = 8

2x – 3y = 5

Bob’s Barbecue sells chopped beef sandwiches for $6 each. Their total profit from making and selling 200 of these sandwiches is $300. They incur fixed costs of $400.

(4 points)

10. Find the linear revenue function for Bob’s Barbecue.

(4 points)

11. Find the linear profit function for Bob’s Barbecue.

Given the equation 5x + 6y = 7, answer the following.

(4 points)

12. What is the equation of the line perpendicular to the given line that goes through the origin?

(4 points)

13. Find the value of a if the line passing through the points (a, 5) and (2, a – 1) is parallel to the line given above.

Are the following matrices (each of which represents a system of equations) in row-reduced echelon form?

IF YES, how many solutions are there to the system? (ONE, NONE, INFINITELY MANY)

IF NO, give the best next Gauss-Jordan operation to be performed. (You do not need to perform the operation.)

(2 points)

14. Row-Reduced? YES or NO (Circle one.)

YES: Number of Solutions? ____________

NO: Next GJ Operation? ______________

(2 points)

15.

Row-Reduced? YES or NO (Circle one.)

YES: Number of Solutions? ___________

NO: Next GJ Operation? _____________

(2 points)

16.

Row-Reduced? YES or NO (Circle one.)

YES: Number of Solutions? ___________

NO: Next GJ Operation? _____________

(12 points)

17. Given the following, find a, b, c, and d. Place your answers in the given box to the right.

[pic]

(8 points)

18. Given the demand equation 3x + p – 40 = 0 and the supply equation 2x – p + 10 = 0 for a particular item, where the unit price is measured in dollars and quantity is measured in units of a hundred, find the equilibrium quantity and equilibrium price.

(6 points)

19. A small town in Texas has a farm and a cattle feed lot with slaughter house. To produce $1 (one unit) worth of beef, they need $0.40 of cattle and $0.20 of produce. To produce $1 (one unit) of produce, they need $0.30 of cattle and $0.20 of produce. The nearby city is demanding $8600 worth of beef and $2800 worth of produce. How much beef and feed need to be produced to meet the internal need and have the necessary exports?

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b =

c =

d =

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