Math 141 Exam 1  Fall '08                   Print Name________________________________

                                                            Section_____

 

1. For the line , each increase of 3 in x produces a change of _____ in y.

 

 

 

2. Circle the line that is parallel to the line .

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3. Demand quantity for a certain product is 1000 units if the price per unit is $45.

Demand is 800 units if the price is $60. Write the linear equation for the demand price, p, and quantity, x.

 

 

 

 

 

 

 

 

4. Demand and supply equations for a certain product are        

and  where p is the price per unit and x is the quantity sold.

Find the equilibrium quantity and price. Show your work.                                 

 

 

 

 

 

 

 

 

 

Equilibrium quantity=______                Equilibrium price= ________

 

 

 

5. The equation of the horizontal line through (2, -3) is ___________.

 

 

    The equation of the vertical line through (2, -3) is _____________.

 

6. A company's total sales in thousands of dollars for each of 4 years are shown.

 

Year     2001    2003    2005    2007

Sales     3.5        4.2        5.1      5.7

 

Let x be the number of years past the year 2000. Find the linear regression equation for the sales and write it without rounding.

 

 

 

 

 

What does the equation predict the sales will be in the year 2008? Do not round.

 

 

 

 

7. For each system of equations, write the solution set or state "no solution".

 

a)              

 

 

 

b)

 

 

 

 

 

 

8. A farmer plants only three crops, corn, wheat and soybeans. Let x be the number of acres of corn, y the number of acres of wheat, and z the number of acres of soybeans. Write an equation in x, y, and z for the statement, "The number of acres of corn is half the total number of acres planted".

 

 

 

 

 

 

 

 

 

9. For what values of c is the matrix in reduced row echelon form?

 

  Circle one answer.

 

a) c=0 only      b) c=1 only          c) c=0 or c=1               d) c can be any number

 

 

 

 

10. For what values of c is the matrix in reduced row echelon form?

 

Circle one answer.

 

a) c=0 only        b) c=1 only        c) c=0 or c=1               d) c can be any number

 

 

 

 

 

11.               Find . You must show work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12.     and where s is an unknown number.

Find .

 

 

 

 

Find X.  Your answer will contain the unknown, s.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13. Perform the next pivot in the row reduction of the augmented matrix,

 

. Label all row operations clearly.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14. A fruit stand owner has $60 with which to purchase strawberries, blueberries, and raspberries. He has 24 square feet of display space for all the fruit. The costs per pint for strawberries, blueberries and raspberries are $0.50, $1.25, and $0.80 respectively.

Each pint uses 0.25 square feet of display space. How many pints of each type of fruit should he buy to use all $60 and all 24 square feet? Define your variables. Give the complete solution set to your system of equations and two reasonable particular solutions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15. A company manufactures widgets, gizmos and doodads. Each widget costs $4 to manufacture, $0.25 to package, and $0.40 to ship. Each gizmo costs $6 to manufacture, $0.50 to package, and $0.60 to ship. Each doodad costs $10 to manufacture, $0.50 to package, and $1.00 to ship. They have an order to manufacture, package and ship 200 widgets, 150 gizmos and 320 doodads.

 

a) Write a matrix product to show the company's manufacturing, packaging and shipping costs. Show the matrices in your product. You do not need to compute the product.

 

 

 

 

 

 

 

 

 

 

 

 

b) Due to wage increases and transportation cost increases, manufacturing costs increase by 50%, packaging costs increase by 20% and shipping costs double. Write a matrix product to show the total cost, under these increases, for the order in part a.

 

 

 

 

 

 

 

 

 

 

 

17.      

 

Solve the matrix equation AX+2X=B    for X.

 

 

 

 

 

 

 

18. An economy is based on 3 sectors; food, clothing and shelter. Production of a dollar's worth of food uses $0.20 of food, $0.05 of clothing and $0.10 of shelter.

Production of a dollar's worth of clothing uses $0.10 of food, $0.20 of clothing and $0.30 of shelter.

Production of a dollar's worth of shelter uses $0.30 of food, $0.10 of clothing and $0.25 of  shelter.

 

a) How many dollar's worth of each sector must be produced to meet a demand for

$1.5 million of food, $3 million of clothing and $7 million of shelter? Use the numbers of millions, for example, 1.5 not 1500000, and round your answers to 3 decimal places.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b) How many dollar's worth of each sector are used in the production of these amounts?