Linear Programming Practice - Algebra 2

A factory makes purses and shoes.  For each purses, you make a $100 profit. For each pair of shoes, you make $50 profit.   A purse takes 3 machine hours and 5 man hours.  A pair of shoes  requires 4 machine hours and 2 man hours.  The machine can operate for up to 50 hours.   The total number of man hours is 60.  How many purses and pairs of shoes should the factory make in order to maximize profits?

Given that X = # of Purses and that Y = # of pairs of shoes

What is the objective function?

A factory makes purses and shoes.  For each purses, you make a $100 profit. For each pair of shoes, you make $50 profit.   A purse takes 3 machine hours and 5 man hours.  A pair of shoes  requires 4 machine hours and 2 man hours.  The machine can operate for up to 50 hours.   The total number of man hours is 60.  How many purses and pairs of shoes should the factory make in order to maximize profits?

Given that x = # of Purses and y = # of pairs of shoes

What inequality represents the constraint of man hours?

A factory makes purses and shoes.  For each purses, you make a $100 profit. For each pair of shoes, you make $50 profit.   A purse takes 3 machine hours and 5 man hours.  A pair of shoes  requires 4 machine hours and 2 man hours.  The machine can operate for up to 50 hours.   The total number of man hours is 60.  How many purses and pairs of shoes should the factory make in order to maximize profits?

Given that x = # of Purses and y = # of pairs of shoes

What inequality represents the constraint of machine hours?

The Wily Monka Chocolate Factory  makes 2 kinds of candies:  Everlasting Goobstoopers and Monka Bars.  The profit for a case of  Everlasting Goob Stoopers is $20.   The profit for a case of Monka Bars is $35.  The goobstoopers have to have 4 machine hours and 5 man hours.  The Monka bar has to have 5 machine hours and 10 man hours.  There are only 410 machine hours and 700 Man hours available.  How many cases of each kind of candy should the factory make to maximize profit?

How would you define your varaibles for this problem?

The Wily Monka Chocolate Factory  makes 2 kinds of candies:  Everlasting Goobstoopers and Monka Bars.  The profit for a case of Everlasting Goob Stoopers is $20.   The profit for a case of Monka Bars is $35.  The goobstoopers have to have 4 machine hours and 5 man hours.  The Monka bar has to have 5 machine hours and 10 man hours.  There are only 410 machine hours and 700 Man hours available.  How many cases of each kind of candy should the factory make to maximize profit?

Given that x = cases od Everlastign Goobstoopers and y = cases of Monka Bars

What is the objective function?

The Wily Monka Chocolate Factory  makes 2 kinds of candies:  Everlasting Goobstoopers and Monka Bars.  The profit for a case of Everlasting Goob Stoopers is $20.   The profit for a case of Monka Bars is $35.  The goobstoopers have to have 4 machine hours and 5 man hours.  The Monka bar has to have 5 machine hours and 10 man hours.  There are only 410 machine hours and 700 Man hours available.  How many cases of each kind of candy should the factory make to maximize profit?

Given that x = cases od Everlastign Goobstoopers and y = cases of Monka Bars

What are the TWO constraint inequalities?

A factory makes soccer balls and basketballs.  The soccer ball requires 4 hours in the fabrication department and the basketball requires 2 hours in the fabrication department.  The soccer ball requires 1 hour in the finishing department and the basketball requires 2 hours in the finishing department.  The fabrication department has 100 hours available per day and the finishing department has 40 hour available per day.  If the profit on the soccer ball is $8 and the profit on the basketball is $10, how many of each should be produced each day to maximize profit?

Define your variables.

A factory makes soccer balls and basketballs.  The soccer ball requires 4 hours in the fabrication department and the basketball requires 2 hours in the fabrication department.  The soccer ball requires 1 hour in the finishing department and the basketball requires 2 hours in the finishing department.  The fabrication department has 100 hours available per day and the finishing department has 40 hour available per day.  If the profit on the soccer ball is $8 and the profit on the basketball is $10, how many of each should be produced each day to maximize profit?

Given that x = # of soccer balls and y = # of basketballs

What is the objective function?

A factory makes soccer balls and basketballs.  The soccer ball requires 4 hours in the fabrication department and the basketball requires 2 hours in the fabrication department.  The soccer ball requires 1 hour in the finishing department and the basketball requires 2 hours in the finishing department.  The fabrication department has 100 hours available per day and the finishing department has 40 hour available per day.  If the profit on the soccer ball is $8 and the profit on the basketball is $10, how many of each should be produced each day to maximize profit?

Given that x = # of soccer balls and y = # of basketballs

What are the TWO inequalities that represent the constraints?

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with barley can be modeled by P=4000x+3000y . If x represents acres of soybeans and y represents acres of corns, which inequalities represent the constraints of the problem?

Select an objective function that models the total profit from cobblers and pies.

A farmer has a field where he can plant either wheat or barley or a combination of both. Each hectare of wheat requires 3 units of water and 2 units of fertilizer, while each hectare of barley requires 2 units of water and 3 units of fertilizer. If the farmer has 15 units of water and 15 units of fertilizer available, which of the following represents the constraint for the fertilizer?