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?

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.

2,160 π

step-by-step explanation: