In Class Exam 1 Review Math 141
1. Find the equation of the line parallel to 8x – 6y = 52 through (3,-1). What is the
slope of this line?
2. Suppliers will supply none of a certain product if the unit price is $350 or less. They
will supply 2000 if the price is $600. Find the linear supply equation.
3. Given two equations 30p + 2x = 18500 and 7p – x = 650 where p is price per unit
and x is quantity, which is the supply equation and which is the demand equatioa)
a) Find the equilibrium quantity and price. Show your work.
b) At what price will no-one buy any?
c) At what price will suppliers provide none?
4. Consumers will buy none of a product at $750 per unit. For each decrease of $50 in the
price, they will buy 200 more units. Find the price as a linear function of quantity. Is this
the demand or the supply equation?
5. A company finds their fixed costs for a certain product total $21000. Each unit costs
and additional $5 to produce and sells for $12. Find the break even quantity and the break
even revenue.
6. Set up but do not solve the following word problem.
A nut mix contains peanuts, cashews, and pecans. Peanuts cost $1.50 per pound, cashews
cost $2.50 per pound, and pecans cost $4.00 per pound. The mix contains 6 pounds and
costs $2.75 per pound. There are half as many pounds of pecans as peanuts and cashews
combined. How many pounds of each does the mix contain?
7. Each augmented matrix is completely reduced and represents a system of equations.
Write the complete solution set for each. If the solution set is infinite, give two particular
solutions.
i)
1 0 2 3 5 
0 1  1 4 7 


1
0
ii) 
0

0
0 2
1 3

0 0

0 0
1 0 1 0


iii) 0 1  2 0


0 0 0 1
a b 
8. A   2 1 
 3  5
a) Find A  2BT
b) Find AC
1 3 1
B

0  1 2
 2 1
C

 3 0
9. A carpenter and his son are building chairs, tables and cabinets. Each chair requires
$20 worth of materials, 10 carpentry hours and 1 finishing hour. Each table requires
$30 for materials, 12 carpentry hours and 3 finishing hours. Each cabinet requires $50
for materials, 16 carpentry hours and 4 finishing hours. They have $300 to spend, 120
hours for carpentry by the father and 21 hours for finishing by the son. How many of
each should they build to use all their resources? Define variables clearly, write the
equations and solve with rref.
10. A meal contains foods A, B and C.. The meal weighs 6 ounces and contains 36
mg of iron. The iron contents per ounce of foods A, B and C are 10 mg, 8 mg and
2 mg respectively. How many ounces of each of A, B and C were used in the meal?
Define variables clearly, write the equations and solve with rref. Give the parametric
solution and two particular, realistic solutions.
11. Same as #10 but require twice as much of B as of A. Give the unique solution.
12. State the rules about matrix sizes for different operations.
Addition can be performed if and only if _________________.
The multiplication AB is possible if and only if ___________________.
If A is mxn then A T is ___________.
If A has an inverse matrix then A is ____________ and _______________.
13. To add the entries in each row (to add up each row) of an mxn matrix, multiply on
the ______________ side by ________________.
To add the entries of each column (to add up each column) of an mxn matrix, multiply
on the ___________ side by __________________.
14. A small town voted on a bond proposal. 70% of republicans voted to pass the bond,
60% of democrats voted to pass it and 55% of independents voted to pass it. The total
numbers of people who voted in each party were 552 republicans, 456 democrats and
98 independents. Write a matrix product that gives the total number of votes in favor of
the bond.
15. a) A person is making cakes, cookies and brownies. Each cake takes 10 minutes
to mix, 60 minutes to bake and 2 minutes to package. Each batch of cookies takes 7
minutes to mix, 30 minutes to bake and 3 minutes to package. Each batch of brownies
takes 10 minutes to mix, 20 minutes to bake and 2 minutes to package. What matrix
product shows the time to mix, the time to bake and the time to package 4 cakes, 6
batches of cookies and 8 batches of brownies?
b) If the costs per minute to mix, bake and package are $.05,
$1.00, and $.03, what matrix product shows the total cost of preparing 4 cakes, 6
batches of cookies and 8 batches of brownies?
16. Perform the next pivot in the row reduction of the augmented matrix shown.
1 0  5 1 
Label each row operation. 0 1 3 4 


0 0 2 10
17. Find the maximum y-value, the minimum y-value, and the x-intercepts of each
quadratic or state DNE if none exists.
a)
y  3( x  4)( x  5)
b)
y  .2 x 2  5 x  24
18.. Find the maximum revenue and maximum profit and the break even quantities for:
The cost function is C ( x)  12 x  600 and the demand equation is p  .2 x  60 .
x=quantity and p=demand price