Exercises 8.0           

Problem 12:
a)	Graph the region of solutions of the given system of linear inequalities
b)	Determine whether the region of solutions is bounded or unbounded
c)	Find all of the regions corner points

5x – y ≥ 7
2x – 3y < -5
                   
Exercises 8.1           

Problem 6:
Convert the information to a linear inequality. Give the meaning of each variable used.

A coffee shop owner has 1,000 pounds of java beans. In addition to selling pure java beans, the shop also sells blend number 202, which is 32% java beans.

Problem 32:
Make up a word problem that results in the following linear programming problem:

Maximize z = 5x + 4y

Subject to the constraints

10x + 20y ≤ 1,000
30x + 10y ≤ 2,000

x ≥ 0  and  y ≥ 0

Exercises 8.2           

Problem 26:
Find the first simplex matrix and the possible solution that corresponds to it. Do not try to solve the problem.

Pete’s Coffees sells two blends of coffee beans: morning Blend and South American Blend. Morning Blend is one third Mexican beans and two-thirds Colombian beans, and South American Blend is two-thirds Mexican beans and one-third Colombian beans. Profit on the Morning Blend is $3 per pound, while profit on the South American Blend is $2.50 per pound. Each day the shop can obtain 100 pounds of Mexican beans and 80 pounds of Columbian beans, and it uses those beans only in the two blends. If it can sell all that it makes, how many pounds of Morning Blend and of South American Blend should Pete’s Coffees prepare each day to maximize profit?
                   
Exercises 8.3           

Problem 14:
Use the simplex method to solve

J & M Winery makes two jug wines, House White and Premium White, which it sells to restaurants. House White is a blend of 75% French colombard grapes and 25% sauvignon blanc grapes, and Premium White is 75% sauvignon blanc grapes and 25% French colombard grapes. J&M also makes a Sauvignon Blanc, which is 100% sauvignon blanc grapes. Profit on House White is $1.00 per liter, profit on the Premium White is $1.50 per liter, and profit on the Sauvignon Blanc is $2.00 per liter. This season, J&M can obtain 30,000 pounds of French colombard grapes and 20,000 pounds of sauvignon blanc grapes. It takes 2 pounds of grapes to make 1 liter of wine. If J&M can sell all that it makes, how many liters of House White, Premium White, and of Sauvignon Blanc should J&M prepare to maximize profit? Would this leave any extra grapes? If so, what amount?
                   
Exercises 9.0B         

Problem 54:
For milk, [H+] = 1.6 x 10-7. Determine the pH and classify milk as acid or base.

Problem 58:
Normally, human blood has a hydrogen ion concentration of about 3.98 x 10-8 moles per liter. Determine the normal pH of human blood. (should be about 7.41)
                   
Exercises 9.1           

Problem 6:
The second largest metropolitan area in the United States is the Los Angeles/Anaheim/Riverside metropolitan area. Its population in 1990 was 14,532 (in thousands); in 2000 it was 16,374.
a)	Convert this information to two ordered pairs (t,p), where t measures years since 1990 and p measures population in thousands.
b)	Find Δt, he change in time
c)	Find Δp, the change in population
d)	Find Δp/Δt, the average growth rate
e)	Find (Δp/ Δt)/p, the relative growth rate

Problem 10:
a)	Develop the model that represents the population of the Los Angeles/Anaheim/Riverside metropolitan area.
b)	Predict the population in 2006
c)	Predict the population 2010
d)	Predict when the population will be 50% more than its 1990 population

Exercises 10.4          

Problem 8:
A tourist drops a penny from the observation platform in the top of the Empire State Building in new York city. It falls 1,248 feet.
a)	How long will it take the penny to hit the ground?
b)	At what speed will the penny be falling when it hits the ground?
c)	What is the average speed of the penny during its journey?
         
Exercises 10.5          

Problem 20:
A firecracker is launched at a 45 degree angle of elevation from ground level with an initial speed of 120 feet per second.
a)	Find the equation of the trajectory of the firecracker
b)	Find the firecracker’s maximum height and the horizontal distance between the launch point and the point of maximum height
c)	Find the amount of time that the fuse should burn if the firecracker is to detonate at the peak of its trajectory.
(HINT: use the answer to part b and “x-equation” that was obtained when we derived the equation of a projectile with a 45 degree angle of elevation)
                   
Exercises 10.6          

For the two following problems, do the following:
a)	Find the area function associated with the given function
b)	Sketch the region whose area is found by that area function
c)	Find A(3), and describe the region whose area is A(3)
d)	Find A(4), and describe the region whose area is A(4)
e)	Find A(4) – A(3), and describe the region whose area is A(4) – A(3)

Problem 2:

f(x) = 6

Problem 4:

f(x) = 4x