A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has atmost Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.

Asked by Last Modified  

5 Answers

Learn Linear Programming

Follow 4
Answer

Please enter your answer

Balmukund Tiwari

Turning Maths, Physics & CS Struggles into Strengths for 100+ Months | B.Tech Grad.

Time constraint: Time = Distance/Speed. Time taken at 50 km/hr is x50\dfrac{x}{50} , and time taken at 80 km/hr is y80\dfrac{y}{80} . Total time available is at most 1 hour: x50+y80≤1\frac{x}{50} + \frac{y}{80} \leq 1 Multiplying through by 400 (LCM of 50 and 80) to clear denominators: 8x+5y≤4008x...
read more
Time constraint: Time = Distance/Speed. Time taken at 50 km/hr is x50\dfrac{x}{50} , and time taken at 80 km/hr is y80\dfrac{y}{80} . Total time available is at most 1 hour: x50+y80≤1\frac{x}{50} + \frac{y}{80} \leq 1 Multiplying through by 400 (LCM of 50 and 80) to clear denominators: 8x+5y≤4008x + 5y \leq 400 Petrol cost is Rs 2 per km at 50 km/hr, and Rs 3 per km at 80 km/hr. Total cost is at most Rs 120: 2x+3y≤1202x + 3y \leq 1208x+5y≤400 ---------- (i)2x + 3y \leq 1202x+3y≤120----------- (ii) read less
Comments
Dislike Bookmark

C Language Faculty (Online Classes ) Having 10 Years Experience

The problem can be formulated as a Linear Programming Problem (LPP) to maximize the total distance \(Z = x + y\), subject to cost and time constraints.Here is the step-by-step mathematical formulation: 1. Decision Variables Let \(x\) be the distance traveled at the speed of 50 km/hour (in km).Let \(y\)...
read more
The problem can be formulated as a Linear Programming Problem (LPP) to maximize the total distance \(Z = x + y\), subject to cost and time constraints.Here is the step-by-step mathematical formulation: 1. Decision Variables Let \(x\) be the distance traveled at the speed of 50 km/hour (in km).Let \(y\) be the distance traveled at the speed of 80 km/hour (in km). 2. Objective Function The goal is to maximize the total distance traveled (\(Z\)).\(\text{Maximize\ }Z=x+y\) 3. Constraints • Petrol Cost Constraint: The cost at 50 km/h is ₹2/km, and at 80 km/h is ₹3/km. The total budget is at most ₹120.\(2x+3y\le 120\)• Time Constraint: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\). The total available time is at most 1 hour.\(\frac{x}{50}+\frac{y}{80}\le 1\)Multiplying by 400 to simplify:\(8x+5y\le 400\)• Non-negativity Constraints: Distance cannot be negative.\(x\ge 0,\quad y\ge 0\) Final LPP Formulation \(\text{Maximize\ }Z=x+y\)Subject to the constraints:• \(2x + 3y \le 120\) (Cost constraint)• \(8x + 5y \le 400\) (Time constraint)• \(x, y \ge 0\) (Non-negativity constraint) read less
Comments
Dislike Bookmark

M.Sc. (Mathematics) | Former Faculty at Vedantu (5 Years) & Doon International School (6 Years)

Let xx be the distance (in km) travelled at 50 km/hour and yy be the distance (in km) travelled at 80 km/hour. 1. Objective function The total distance travelled is x+yx+y. Since he wants to travel the maximum distance, the objective function...
read more
Let xx be the distance (in km) travelled at 50 km/hour and yy be the distance (in km) travelled at 80 km/hour. 1. Objective function The total distance travelled is x+yx+y. Since he wants to travel the maximum distance, the objective function is MaximizeZ=x+yMaximizeZ=x+y 2. Constraints Petrol cost constraint: At 50 km/hour, the cost is Rs 2 per km, and at 80 km/hour, it is Rs 3 per km. The total petrol budget is at most Rs 120. 2x+3y≤1202x+3y≤120 Time constraint: Time taken at 50 km/hour is x5050x hours, and at 80 km/hour is y8080y hours. The total time available is at most 1 hour. x50+y80≤150x+80y≤1 Multiplying by 400 gives 8x+5y≤4008x+5y≤400 Non-negativity constraints: x≥0,y≥0x≥0,y≥0 Final answer: Linear Programming Problem (LPP) Maximize Z=x+yZ=x+y Subject to the constraints 2x+3y≤1208x+5y≤400x,y≥02x+3y8x+5yx,y≤120≤400≥0 read less
Comments
Dislike Bookmark

Turning Maths, Physics & CS Struggles into Strengths for 100+ Months | B.Tech Grad.

Let x = km at 50 km/h, y = km at 80 km/h. Maximise Z = x + y subject to: 2x + 3y ≤ 120 (petrol) 8x + 5y ≤ 400 (time: x/50 + y/80 ≤ 1) x ≥ 0, y ≥ 0 (Maximum Z = 380/7 ≈ 54.29 km, at x = 300/7, y = 80/7.)
read more
Let x = km at 50 km/h, y = km at 80 km/h. Maximise Z = x + y subject to: 2x + 3y ≤ 120 (petrol) 8x + 5y ≤ 400 (time: x/50 + y/80 ≤ 1) x ≥ 0, y ≥ 0 (Maximum Z = 380/7 ≈ 54.29 km, at x = 300/7, y = 80/7.) read less
Comments
Dislike Bookmark

Turning Maths, Physics & CS Struggles into Strengths for 100+ Months | B.Tech Grad.

Let x = distance (km) travelled at 50 km/h and y = distance (km) travelled at 80 km/h. Maximise Z = x + y Subject to: Petrol cost: 2x + 3y ≤ 120 Time: x/50 + y/80 ≤ 1, which simplifies to 8x + 5y ≤ 400 x ≥ 0, y ≥ 0 (Multiplying x/50 + y/80 ≤ 1 by 400 gives 8x + 5y ≤...
read more
Let x = distance (km) travelled at 50 km/h and y = distance (km) travelled at 80 km/h. Maximise Z = x + y Subject to: Petrol cost: 2x + 3y ≤ 120 Time: x/50 + y/80 ≤ 1, which simplifies to 8x + 5y ≤ 400 x ≥ 0, y ≥ 0 (Multiplying x/50 + y/80 ≤ 1 by 400 gives 8x + 5y ≤ 400.) read less
Comments
Dislike Bookmark

View 3 more Answers

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Recommended Articles

The Trend of E-learning and it’s Benefits

E-learning is not just about delivering lessons online. It has a much broader scope that goes beyond manual paper or PowerPoint Presentations. To understand the reach of E-learning and how the whole process works in developing the Educational system, we will discuss a few points here. Let us find out how this new learning...

Read full article >

Science, Arts Or Commerce - Which One To Go For?

Once over with the tenth board exams, a heavy percentage of students remain confused between the three academic streams they have to choose from - science, arts or commerce. Some are confident enough to take a call on this much in advance. But there is no worry if as a student you take time to make choice between - science,...

Read full article >

5 Engaging Activities For Children To Get...

Learning for every child starts from a very young age. While the formal methods include school curriculums and private lessons, the informal methods include dancing, music, drawing, and various fun-filling activities. Playing games and practising these types of activities helps the children get out of boredom and...

Read full article >

How To Choose The Right School For Children?

Quality education does not only help children to get a successful career and life, but it also hugely contributes to society. The formal education of every child starts from school. Although there are numerous schools, parents find it challenging to choose the right one that would fit their child. It is difficult for them...

Read full article >

Find Tuition near you
Tuition in Delhi
Tuition in Bangalore
Tuition in Hyderabad
Tuition in Kolkata
Tuition in Chennai
Tuition in Mumbai
Tuition in Lucknow
Tuition in Pune
Tuition in Noida
Tuition in Jaipur
Online Tuition Classes

Looking for Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you