MATH 1324 HCCS Graph Your Constraints and Find the Solution Math Questions

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