Creating Objective Equation Linear Programming

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?
   

• maximum value at (5, 4); 32

• maximum value at (0, 8); 16

• maximum value at (9, 0); 27

• maximum value at (0, 0); 0

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

• x + y ≤ 8

• x + y ≤ 6

• 2x + 3y ≤ 6

• x + y ≤ 10

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

• P = 30x + 50y

• P = 50x + 30y

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective function?

• P(x, y) = 30x + 50y

• P(x, y) = 50x + 30y

The FFA Club plans to grow Christmas trees as a project. There is a 1200 square foot plot of land available at their school to grow balsam fir and Douglas fir trees. There are only 576 pounds of fertilizer available. The profit for each balsam fir tree is $15 and $18 for each Douglas fir tree. Which of the following is an Objective Function that relates maximum profit?

• P = x + y

• P = 576x + 1200y

• P = 15x + 18y

• P = 1200x + 576y

It is a method for finding a maximum or minimum value of some quantity, given a set of constraints.

• Operations research

• Maximization

• Minimization

• Linear programming

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

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 possible solutions to her situation?

• x≥0

  y≥0

  x+y≥6

  3x+2y≥15

• x≥0

  y≥0

  x+y≤6

  2x+3y≤15

• x≥0

  y≥0

  4000x+y≤6

  2x+600y≤15

• P=4000x+3000y

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

• 300

• 280

• 400

• 240