S1-5
S1: Suppose that a principal of $3,000 is deposited for 8 years in a savings account at 4.5% compounded quarterly. How much money would be the balance savings account after 8 years?
$4,291.35
S6: Suppose that the demand curve for corn has the equation p=-.16q+4.68 and the supply curve for corn has the equation p=.44q+3.48, where p is the price per bushel in dollars and q is the quantity (demand or produced) in billions of bushels. Determine the equilibrium quantity of corn that will be produced and the price at which it will sell.
The equilibrium is 2 billion bushels at $4.36 per bushel
S11: In a certain state legislature the percentage of legislators voting for or against lowering the legal drinking age by various party affiliations is summarized by this matrix.
Democrat .5 .5
Republican .2 .8
Independent 0 1
There are 50 Democratic, 20 Republicans, and 10 Independents in the legislature. Use a matric calculation to determine how many legislators voted for lowering the drinking age and how many voted against lowering the drinking age.
29 voted for
51 voted against
S16:
A small manufacturing plant produces two kinds of bicycles - 1-speed and 10-speed. The plant can manufacture up to 400 of the 1-speed bicycles and up to 500 of the 10-speed bicycles per month, but it can only manufacture 650 of both kinds in all every month. It takes 40 man-hours to manufacture a 1-speed bicycle and 80 man-hours for the 10-speed; there are 44,000 man-hours available per month. The profit of the 1-speed bicycles is $20 and the profit of the 10-speed bicycle is $30.
Set up this problem as a linear programming problem.
x= # of 1-speed bicycles
y=# of 10-speed bicycles
0<=x<=400
0<=y<=500
x+y<=650
40x+80y<=44,000
Profit = 20x+30y
S21: Maximize 3000x+5000y
x<=4
2y<=12
3x+2y<=18
x>=0; y>=0
Maximized at 36000
GI: v=0, w=0
GII: x=2, y=6, u=2, M=36000
S2: Mr. Pod deposits $2500 at the end of each month for 6 years into a savings account paying 3.4% interest compounded monthly. However, he deposited an additional $4,000 at the end of the fourth year. How much money was in the account at the end of the 6th year?
$204,266.55
S7: The sales division of a company purchased type A cell phones for $595 each and type B cell phones for $510 each. It purchased a total of 18 cell phones at a total cost of $10030. Write this in a system of linear equations.
x= # of type A cell-phones
y=# of type B cell-phones
x+y=18
595x+510y=10,030
S12: Calculate the inverse of
2 3
2 2
-1 3/2
1 -1
S17: Consider the FS of a graph on Desmos of a certain linear programming problem. Find all possible vertices and state what is the maximum value of the objective function 2500x+4500y
The maximum value is $90,000 when x=0 and y=20.
S22: A company makes 3 brands of TV sets, A, B, and C in 2 different plants, plant I and II. Plant I has a production capacity of 40 brand-A sets, 40 brand-B sets, and 20 brand-C sets with a daily operating cost of $3000. Plant II has a production capacity of 20 brand-A sets,60 brand-B sets. and 20 brand-C sets with a daily operating cost of $2000. How many days should each plant be operated to fill and order of 600 brand-A, 1000 brand-B, and 400 brand-C sets at the minimum cost?
Each Plant should operate 10 days with a minimum cost of $50,000.
S3: When Remigia takes a new job, she is offered a choice of a $5,250 bonus now or extra $450 at the end of each month for the next year. Assume that the money can earn an interest rate of 4.2% compounded monthly.
a) What is the value of the $5,250 at the end of one year.
b) What is the value of $450 at the end of each month for 12 months?
c) Which option should Remigia choose?
a) $5,474.79
b) $5,505.17
c) Remigia should take the $450 at the end of each month option.
S8: The sales division of a company purchased type A cell phones for $595 each and type B cell phones for $510 each. It purchased a total of 18 cell phones at a total cost of $10030. How many type A and type B cell phones did the division purchase? (Solve the system using Gauss and Jordan elimination method.)
They bought 10 type A and 8 type B cell phones.
S13: Solve using the inverse of a matrix
2x+3y=6
4x+5y=8
x=-3
y=4
S18: Add slack variables to the following set of inequalities:
x+3y<=10
-2x-5y<=145
35x-.5y<=13
x+3y+u=10
-2x-5y +v=145
35x-.5y +w=13
S23: Draw a 3 circle Venn Diagram and shade the portion corresponding to the set (TuR)'nS'
Share Screen
S4: Joan wants to start an IRA that will have $600,000 in it when she retires in 38 years. How much should she invest annually in her IRA to do this if the interest is 3.3% compounded annually?
$8,134.44
S9: Write all the solutions of the linear equations given in the following augmented matrix.
-2 0 1 13
0 1 -2 7
0 0 0 3/2
No solutions!
S14: Graph and shade 2x-y>=5.
y<=2x-5
*Desmos 2x-y<=5*
S19: Which element do we pivot?
1 0 3 2 16 0 9
0 1 4 8 2 0 5
0 0 -6 3 0 1 -40
Element 4
S24: A bag contains 12 carrots and 9 peach. If you select 8 pieces of fruit without looking , how many ways can you get exactly 4 peaches?
There are 34650 ways to get exactly 4 peaches.
S5: Graph 6x+y=6 by finding the x-intercept and the y-intercept.
x-intercept: (1,0)
y-intercept: (0,6)
*Desmos 6x+y=6*
S10: What are the three arithmetic operations on matrices that we can preform?
1. Switch rows and columns.
2. Multiply a row by a constant.
3. Add or subtract a multiple of one row to another.
S15: Graph the feasible set
x+y<=5
-2x+3y<=12
x>=0; y>=0
*Desmos*
S20: How do we know we are done pivoting the Tableau of the Simplex Method?
1. No negatives in the last row.
2. No negatives in the last column not including the last entry.
S26: Of the 80 people who answered "yes" to a question, 28 were male. of the 70 people who answered "no" to the question, 25 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?
There is a 70% chance that the person answered "yes" or was male.