This is math for social and business science. Please use desmos graphing calculator to graph the solutions.

https://www.desmos.com/calculator

. put all equations in slope intercept form and then put it in the calculator to graph. Math 1324 Chapter 7 Project

Name_________________________

You solve problem #1 and either 2 or 3. You will create a linear optimization model for

each problem. You will graph your constraints and find the solution. You must include

your Objective Function and Constraints for each problem. You must include a copy of

your graph (you can use a screen shot). You must explain your solution.

Rubric:

Problem # 1

Points

Variables are clearly and accurately defined

Constraint inequalities are clearly and accurately written

Objective Function is clearly and accurately written

A neat and well labeled graph of constraints is shown

Analysis of the objective is accurate and clear

An accurate and clear conclusion statement is given.

Total points

Possible

Points

5

10

10

10

10

5

50

Problem #______________

Points

Variables are clearly and accurately defined

Constraint inequalities are clearly and accurately written

Objective Function is clearly and accurately written

A neat and well labeled graph of constraints is shown

Analysis of the objective is accurate and clear

An accurate and clear conclusion statement is given.

Total points

Possible

Points

5

10

10

10

10

5

50

1. The Healthy Pet Food Company manufactures two types of dog food: Meaties

and Yummies. Each package of Meaties contains 2 pounds of cereal and 3

pounds of meat; each package of Yummies contains 3 pounds of cereal and 1.5

pounds of meat. Healthy believes it can sell as much of each dog food as it can

make. Meaties sell for $2.80 per package and Yummies sell for $2.00 per

package. Healthy’s production is limited in several ways. First, Healthy can buy

only up to 400,000 pounds of cereal each month at $0.20 per pound. It can buy

only up to 300,000 pounds of meat per month at $0.50 per pound. In addition, a

special piece of machinery is required to make Meaties, and this machine has a

capacity of 90,000 packages per month. The variable cost of blending and

packing the dog food is $0.25 per package for Meaties and $0.20 per package

for Yummies. This information is given in the table.

Sales price per package

Raw materials per package

Cereal

Meat

Variable cost—blending and

packing

Production capacity for Meaties

Cereal available per month

Meat available per month

Meaties

$2.80

Yummies

$2.00

2 lbs.

3 lbs

$0.25

3 lbs.

1.5 lbs

$0.20

90,000 packages per month

400.000 lbs.

300,000 lbs.

2. Dorian Auto manufactures luxury cars and trucks. The company believes that its

most likely customers are high-income women and men. To reach these groups,

Dorian Auto has embarked on an ambitious TV advertising campaign and has

decided to purchase 1-minute commercial spots on two types of programs:

comedy shows and football games. Each comedy commercial is seen by 7

million high-income women and 2 million high income men. Each football

commercial is seen by 2 million high-income women and 12 million high-income

men. A 1-minute comedy ad costs $50,000, and a 1-minute football ad costs

$100,000. Dorian would like the commercials to be seen by at least 28 million

high-income women and 24 million high-income men. Use linear programming to

determine how Dorian Auto can meet its advertising requirements at minimum

cost.

3. Farmer Jane owns 45 acres of land. She is going to plant each with wheat or

corn. Each acre planted with wheat yields $200 profit; each with corn yields $300

profit. The labor and fertilizer used for each acre are given in the table. One

hundred workers and 120 tons of fertilizer are available. Use linear programming

to determine how Jane can maximize profits from her land.

Labor

Fertilizer

Wheat

3 workers

2 tons

Corn

2 workers

4 tons

The price is based on these factors:

Academic level

Number of pages

Urgency

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- Unlimited revisions
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On-demand options

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Paper format

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- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

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