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- 1. Multiple Choice
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
- 2. Multiple Choice
In other words...what are the vertices of the feasible region?
(0, 0), (0, 6), (6, 2), (8, 0)
(0, 0), (6, 0), (2, 6), (0, 8)
- 3. Multiple Choice
When graphing constraints, what do you call the area where all the shading overlaps?
the answer
the feasible region
the void
the objective function
- 4. Multiple Choice
Given the objective function: P = 30x + 50y
Which vertex maximizes the profit?
(0,0)
(6,2)
(8,0)
(0,6)
- 5. Multiple ChoiceFind 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); 32maximum value at (0, 8); 16maximum value at (9, 0); 27maximum value at (0, 0); 0 - 6. Multiple Choice
Which corner point will maximize the Objective Function
(7,4)
(3,10)
(10,1)
(8,5)
- 7. Multiple ChoiceA 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 he plants and $3,000 for every acre he 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≥15x≥0
y≥0
x+y≤6
2x+3y≤15x≥0
y≥0
4000x+y≤6
2x+600y≤15P=4000x+3000y - 8. Multiple ChoiceA 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 he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y . What is the maximum profit that she can earn?$15,000$21,000$18,000$25,000
- 9. Multiple ChoiceA 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 he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y . What combination of soybeans and corn will maximize profit?4 acres of soybeans and 2 acres of corn6 acres of soybeans and 0 acres of corn3 acres of soybeans and 3 acres of corn0 acres of soybeans and 5 acres of corn
- 10. Multiple Choice
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 > 8
2x + 3y ≤ 6
x + y ≤ 10
- 11. Multiple ChoiceIt 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 ≤ 18x + y ≤ 6x + y ≤ 93x + 2y ≤ 18
- 12. Multiple Choice
Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective function?
P = 30x + 50y
P = 50x + 30y
- 13. Multiple Choice
Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the corner points?
(2, 0), (4, 5), (6, 0)
(2, 0), (3, 5), (0, 6)
(0, 2), (3.5, 4.5), (6, 2)
(0, 0), (3, 5), (6, 0)
- 14. Multiple Choice
Maximize P = 3x + y with the following constraints:
x = 0, y = 300
x = 150, y = 150
x = 100, y 150
x = 150, y = 100
- 15. Multiple Choice
Solve the system of inequalities. The feasible region is shown by the darkest blue shading.
- 16. Multiple ChoiceGraph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region.
3 ≤ y ≤ 6
y ≤ 3x + 12
y ≤ -2x + 6
f(x , y) = 4x - 2yThe maximum value is 0 at (0, 6). The minimum value is - 20 at (-3, 3).The maximum value is 0 at (-3, 3). The minimum value is - 20 at (0, 6).The maximum value is 0 at (-2, 6). The minimum value is - 20 at (1.5, 3).The maximum value is 0 at (1.5, 3). The minimum value is - 20 at (-2, 6). - Answer choicesTagsAnswer choicesTags