Maximizing Farm Profit Using Linear Programming

The video tutorial explains how a farmer can maximize profit by dividing a 50-acre farm between two crops using linear programming. It defines variables for the number of acres for each crop, sets up a profit equation, and lists constraints based on cost and acreage. The tutorial then demonstrates graphing the constraints to find the feasible region and calculates the maximum profit by evaluating the vertices of this region.

What is the maximum amount the farmer can spend on seeds?

• $600

• $500

• $700

• $800

Which crop provides a higher profit per acre?

• Crop A

• Crop B

• Both provide the same profit

• Neither provides a profit

What is the objective function used to calculate profit?

• P = 100a + 200b

• P = 140a + 150b

• P = 150a + 140b

• P = 200a + 100b

What is the total acreage constraint for the farm?

• a + b ≤ 60

• a + b ≤ 50

• a + b ≤ 70

• a + b ≤ 40

What is the cost constraint equation for the seeds?

• 10a + 20b ≤ 600

• 10a + 20b ≤ 700

• 10a + 20b ≤ 800

• 10a + 20b ≤ 900

What does the feasible region represent in this problem?

• The area where profit is minimized

• The area where costs are maximized

• The area where all constraints are satisfied

• The area where no constraints are met

Which point is NOT a vertex of the feasible region?

• (0, 35)

• (40, 10)

• (50, 0)

• (0, 0)

How is the intersection point of two lines found algebraically?

• By drawing a graph

• By using a calculator

• By solving a system of equations

• By guessing

What is the maximum profit the farmer can achieve?

• $7,200

• $6,000

• $8,000

• $7,000

How many acres of crop A should be planted to achieve maximum profit?

• 20 acres

• 50 acres

• 40 acres

• 30 acres