Question

During the month of July, Pittsburgh resident B. Fly must make four round-trip flights between Pittsburgh and

Chicago. The dates of the trips are as shown in Table 87. B. Fly must purchase four round-trip tickets. Without a discounted fare, a round-trip ticket between Pittsburgh and Chicago costs $500. If Fly’s stay in a city includes a weekend, then he gets a 20% discount on the round-trip fare. If his stay in a city is at least 21 days, then he receives a 35% discount; and if his stay is more than 10 days, then he receives a 30% discount. Of course, only one discount can be applied toward the purchase of any ticket. Formulate and solve an assignment problem that minimizes the total cost of purchasing the four round-trip tickets. (Hint: Let xij 1 if a round-trip ticket is purchased for use on the ith flight out of Pittsburgh and the jth flight out of Chicago. Also think about where Fly should buy a ticket if, for example,x21 1.)

Leave Pittsburg Leave Chiago
Monday, July 1 Friday, July 5
Tuesday, July 9 Thursday, July 11
Monday, July 15 Friday, July 19
Wednesday, July 24 Thursday, July 25

Answer 1

Answer:

$1,450

Explanation:

I have used the software WinQsb to solve this assignment problem.

Step 1: Run WInQsb and clock on "Network modelling"

Step 2: Open the next window, select "Assignment Problem" and "Minimization", then enter the variables number and constraints number, as shows the attached image 1.

Step 3: Enter the values, considering: 80% (100% - 20%) of $500 is $400; 65% (100% - 35%) of $500 is $325; 70% (100% - 30%) of $500 is $350. See the attached image 2.

Step 4: Go to "Solve and Analyze" and click on "Solve the problem", so you will obtain the results as shows the attached image 3.

Now, you can see that the total cost of purchasing the four round trip minimized costs is $1,450.

Hope this helps!