Maximization by the simplex method

Solve the following linear programming problems using the simplex method.

1>.

Maximize z = x₁ + 2x₂ + 3x₃

subject to x₁ + x₂ + x₃ ≤ 12

2x₁ + x₂ + 3x3 ≤ 18

x₁, x_2, x₃ ≥ 0

2>.

A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?

diameter: 1.90, 3.30, 4.23, 6.04 and 6.60 and their corrosponding circumferences are 5.93, 10.45, 13.30, 18.45 and 21.20 respectively (Note: both are measured in centimeters). Now, use these data to obtain the following:

1. Plot c vs. d, obtain the equation of straight line and list the value of slope.

2. Perform the LINEST, and hence find the slope, the uncertainty in slope, y-intercept and the uncertainty in y-intercept.

3. Finally, find the % error in pi by comparing the slope from linest with the known value of pi (=3.14).

How can you determine if two lines are parallel, perpendicular, or neither ?

Test Review

Part I

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-3x-9) + 1.

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-3x+9) + 4

Part II

Convert the complex number from rectangular form to polar form. Show all work for full credit.
z = -14 + 8i

Solve for all roots of the equation. Show all work for full credit.
x³ + 216 = 0

a.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=1/x, y=0, y=0, x=1, x=1, and x=3x=3 about the xx-axis.

b.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 and y^2=x about the x-axis.

c.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves x= y - y^2 and x= 0 about the y-axis

d.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y^2= x and x = 2y about the y-axis

e.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y = x ,y= 0, x = 2, and x= 4 about the line x = 1

e.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y = x and y= sqrt(x)

Question : y'''+4y' =0 , y'''-2y''+4y'-8y=0 , y'''-3y''+3y'-y=0 , y^4 -4y'''+6y''-4y+y=0 , y^4+6y''+9y=0 , y^6+y'''=0

Question 1

a. cos Ѳ =-24/25, Ѳ in quadrant 3, find sin Ѳ

b. sin Ѳ=12/13, Ѳ in quadrant 2, find cos Ѳ

c.cos Ѳ =12/13,270 degrees<Ѳ <360 degrees, find sin Ѳ

d.find the reference angle for 279 degrees

Geometric Nets

Suppose you could split open and flatten an ice cream cone.

Before doing so, you measure the circumference around the top of the cone and find it is 9.4 inches.

What is the radius of the opening of the cone approximated to the nearest tenth of an inch?Explain your answer.

Draw a picture of the flattened cone.

Explain how the circumference of the cone translates to the shape of your drawing.

A thermometer is taken from a room where the temperature is 23oC to the outdoors, where the temperature is −1oC. After one minute the thermometer reads 15oC.
(a) What will the reading on the thermometer be after 5 more minutes?

(b) When will the thermometer read 0oC? ________ minutes after it was taken to the outdoors.

A tank contains 220 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 8 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate.
(a) How much sugar is in the tank at the begining? y(0)=___ kg

(b) Find the amount of sugar after t minutes. y(t)=___ kg

(c) As t becomes large, what value is y(t) approaching ? In other words, calculate the following limit. limt→∞y(t)=____ kg

A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $20 per acre. Seed for crop B costs $40 per acre. The farmer can spend at most $2200 on seed.

If crop B brings in a profit of $320 per acre, and crop A brings in a profit of $140 per acre, how many acres of each crop should the farmer plant to maximize her profit?