Question

Ben works for software company in Cleveland. To train new employees, Ben travels to their two other locations, Buffalo and Philadelphia. A Buffalo trip takes two days while a Philadelphia trip takes three days. He can travel no more than 105 days each year. Due to many new employees this year, he must ravel to Phildelphia at least 5 times and Buffalo at least 15 times. It costs the company $180 for each Buffalo trip and $300 for each Philadelphia trip. How many times should Ben travel to buffalo and Philadelphia to minimize costs to the company?

Answer 1

Answer:

Explanation:we will solve this question with help of linear programming.

Now,  let Ben goes x times in buffalo trip and goes y times in Philadelphia trip. Thus, according to the question, Min Z= 180x+300y

And s.t.r. 2x+3y≤105, where x≥5, y≥15.

since at (0,0) 0≤105(true), so area of 2x+3y≤105 will cover the origin.

But, 0≥5 and 0≥15 are false, so their area will not cover the origin.

Thus, after drawing the graph of these three lines we will get a feasible reason of triangle ABC, where point A≡(5,31.667), B≡(5,15), and C≡(30,15)

Z at A- 180×5+300×31.667=10,400.1

at B-180×5+300×15=1350( which is minimum.)

at C- 180×30+300×15=5,850

Thus, Ben should go 5 times to buffalo trip and 15 times to Philadelphia to minimize his cost which is $1350.