How to solve a word problem for linear programming

The video tutorial addresses a scheduling problem for a doctor who needs to allocate time for routine office visits and full physicals. The goal is to maximize income given constraints on time and the number of physicals. The instructor defines variables, explains constraints, and uses graphing to find the feasible region. By evaluating vertices, the solution shows that maximizing office visits yields the highest income.

What are the two types of appointments the doctor can schedule?

• Routine office visits and emergency visits

• Consultations and emergency visits

• Full physicals and consultations

• Routine office visits and full physicals

How many minutes does a routine office visit take?

• 45 minutes

• 30 minutes

• 15 minutes

• 60 minutes

What is the maximum number of full physicals the doctor can perform in a day?

• 15

• 10

• 5

• 20

What is the total available time in minutes for appointments each day?

• 480 minutes

• 540 minutes

• 600 minutes

• 720 minutes

What is the equation used to represent the time constraint for office visits and physicals?

• 15X + 45Y < 540

• 15X + 45Y ≤ 540

• 15X + 45Y = 540

• 15X + 45Y ≥ 540

What is the slope of the line representing the time constraint after simplification?

• -1/3

• -3

• 3

• 1/3

Which point is a vertex of the feasible region?

• (36, 0)

• (10, 10)

• (0, 36)

• (0, 0)

What is the income from 36 office visits?

• $3600

• $6000

• $1000

• $2160

What is the maximum income the doctor can achieve?

• $3600

• $2160

• $1360

• $1000

What should the doctor focus on to maximize income?

• Performing more office visits

• Increasing the cost of physicals

• Performing more physicals

• Reducing the number of appointments