Write an objective function for CD sales) (Hint: Think about how each TV) ((x)) and magazine (y) ads affects sales.)
Substitute the coordinates of the vertices into the objective function.
What is the maximum sales in dollars and at what ordered pair did this occur?
Knowing this information, how many TV and magazine ads should you buy?

Topic:

Linear Functions

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Question 10

22. A bridge constructed over a bayou has a supporting arch in the shape of a parabola. Find a equation of the parabolic arch if the length of the road over the arch is 100 meters and th maximum height of the arch is 40 meters.

Topic:

Quadratic Functions

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Question 11

An object is thrown upward at a speed of 108 feet per second by a machine from a height of 7 feet off the ground. The height

h

of the object after

t

seconds can be found using the equation

h = - 16 t^{2} + 108 t + 7

When will the height be 132 feet?
Select an answer
When will the object reach the ground?
Select an answer $\lor$

Topic:

Quadratic Functions

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Question 12

Name: Wenc L Lodiscu Date:

2/9/23

Linear ModeLing COMMON CORE ALGEBRA II HOMEWORK APPLICATIONS 1. Which of the following would model the distance,

D

, a driver is from Chicago if they are heading towards the city at 58 miles per hour and started 256 miles away? (1)

D = 2561 + 58

(3)

D = 58 t + 256

(2)

D = 256 - 58 x

(4)

D = 58 - 256 t

2. The cas

C

, of prodecing

x

-thies is given by

C = 22 x + 132

. The revenue gained from selling

x

-bikes is given by

R = 350

. If the prost,

P

, is defined as

P = R - C

, then which of the following is an equation for

P

in terisis of

x

? (1)

P = 328 x - 132

(3)

P = 328 z + 132

(2)

P = 372 x + 132

3. The average temperature of the plineci is expected to rise at an average rate of

0.04

degrees Celsius per year due to globel warming, The averpge ecemperature in the year

2000 was 14.71

de grees Celsius. The average Celsus temperature,

C

, is given by

C = 14.71 + 0.04 x

, where

x

represents the number of years since 2000 .

What will be the average temperature in the
Algebraically determine the number of year 2100 ? years, $x$ , it will take for the temperature, $C$ , to reach 20 degrees Celsius. Round to the nearest year.
Sketch a graph of the average yearly temperature below for the interval $0 \leq x \leq 200$ . Be sure to label your $y - 2 x i s$ scale as well as two points on the line (thic $y$ -intercept and one additional point).
What does this model projost to be the average global temperabure in 2 in 0 ? Whähistrucnow, Reo Hoox, NY 12571, 02015

Topic:

Linear Functions

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Question 13

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set of the equation

x^{6} + 63 x^{3} - 64 = 0

is (Use a comma to separate answers as needed.) B. There are no real solutions.

Topic:

Polynomial Functions

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Question 14

Find the real solutions by factoring.

3 x^{3} + 16 = x^{2} + 48 x

Select the correct choice below and fill in any answer boxes within your choice. A. The solution set is (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. There are no real solutions.

Topic:

Polynomial Functions

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Question 15

Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.

6 - 4 (1 - x) \leq 5

Express the solution using set-builder notation. The solution set is

{x ∣ □}

(Use integers or fractions for any numbers in the expression.)

Topic:

Linear Functions

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Question 16

A two variables linear programming problem (100 points) A utility company supplies drinking water to a community, which demands at least

10, 000 m^{3}

of water daily, from two pumping stations (

A

and C). Station A has a maximum supply capacity of

18, 000 m^{3}

, while station

C

has a maximum capacity of

20, 000 m^{3}

per day. Due to operational constraints, station

C

must supply at least

6, 000 m^{3}

of water. In addition, since both stations handle different purity levels, the water authority stated that the amount of water supplied by station

A

must be at least one-third of the amount supplied by station

C

. The operational costs of supplying one cubic meter

(m^{3})

of water from the stations are 2000\left(\ / m^{2}\right)

f ro m A an d

1000\left(\ / m^{2}\right) from C. Please formulate a linear programming model that allows finding the optimal way to meet the community's water demand at the lowest possible cost, while complying with the system's requirements. The following questions need to be answered (elaborate on your answers):

(10 points) Formulate the optimization model for this problem: define the decision variables, objective function, and constraints;
(5 points) Solve the problem graphically: draw the feasible region, evaluate its corner points, and point out the optimal solution;
(5 points) Classify the constraints into active and non-active.
(10 points) The company is considering expanding the supply capacity of one of the two stations and wants you to make a recommendation in this regard, Write: which station to expand and by what amount?
(10 points) How much would the total costs increase if the capacity of station A were reduced by half, that is, $9000 m^{3}$ , and explain why?