Linear Programming Practice Problems

For the given objective function, find the maximum value subject to the constraints. Hint: first graph the region enclosed by the constraints.
Function: z = 5x+y
Constraints:
x+y ≤ 1
x-y ≤ 1
y ≥ 0
x ≥ 0

For the given objective function, find the maximum value subject to the constraints. (Hint: first graph the region enclosed by the constraints.)

Function: z = 6x + 13y
Constraints:
2x+3y ≥ 9
3x+2y ≤ 13
y ≤ x
y ≥ 0
x ≥ 0

For the graphed region shown, determine the value of the objective function z = 5x+4y at each of its corners. What are the minimum and maximum values of the objective function?

a) minimum = 2, maximum = 40

b) minimum = 0, maximum = 25

c) minimum = 0, maximum = 52

d) minimum = 2, maximum = 35

Evaluate the objective function, z, at the vertices of the graph of the region of feasible solutions, and determine the maximum and minimum values of the function:

z = 5x + 8y 

Find the maximum and minimum values of the objective function, z, by considering the graph of the region of feasible solutions:
z = 5x + 8y 

Evaluate the objective function, z, at the vertices of the graph of the region of feasible solutions, and determine the maximum and minimum values of the function:

z = 14y 

A farmer wants to plant a combination of corn and wheat on his farm. He wants to plant at least 30 acres of corn and at least 40 acres of wheat. He has two types of seeds available: Seed A and Seed B. Each acre of Seed A yields 120 bushels of corn and 40 bushels of wheat, while each acre of Seed B yields 150 bushels of corn and 30 bushels of wheat. The farmer has a maximum of 800 acres available for planting. Write a system of inequalities to represent the farmer's constraints and graph the feasible region.

Evaluate the objective function, z = 2x + 4y, at each corner of the graphed region. Then, determine its maximum and minimum value.  

Evaluate the objective function, z = 25x + 60y, at each corner of the graphed region. Then, determine its maximum and minimum value. 

Graph the following system of inequalities, and evaluate the objective function at each corner of the graphed region. Then, identify the values of x and y for which the maximum value is found.

Graph the following system of inequalities, and evaluate the objective function at each corner of the graphed region. Then, identify the values of x and y for which the maximum value is found.

Graph the following system of inequalities, and evaluate the objective function at each corner of the graphed region. Then, identify the values of x and y for which the maximum value is found.

Graph the following system of inequalities, and evaluate the objective function at each corner of the graphed region. Then, identify the values of x and y for which the maximum value is found.