D2 June 2007 Q4

EdexcelOld spec16 marksTransportation Problems

4. A group of students and teachers from a performing arts college are attending the Glasenburgh drama festival. All of the group want to see an innovative modern production of the play ‘The Decision is Final’. Unfortunately there are not enough seats left for them all to see the same performance.

There are three performances of the play, 1, 2, and 3. There are two types of ticket, Adult and Student. Student tickets will be purchased for the students and Adult tickets for the teachers.

The table below shows the price of tickets for each performance of the play. There are 18 teachers and 200 students requiring tickets. There are 94, 65 and 80 seats available for performances 1, 2, and 3 respectively.

AdultStudent
Performance 1£5.00£4.50
Performance 2£4.20£3.80
Performance 3£4.60£4.00
(a) Complete the table below.
AdultStudentDummySeats available
Performance 1£5.00£4.50
Performance 2£4.20£3.80
Performance 3£4.60£4.00
Tickets needed

(2)

(b) Explain why a dummy column was added to the table above. (1)
(c) Use the north-west corner method to obtain a possible solution. (1)
(d) Taking the most negative improvement index to indicate the entering square, use the stepping stone method once to obtain an improved solution. You must make your shadow costs and improvement indices clear. (6)

After a further iteration the table becomes:

AdultStudentDummy
Performance 17321
Performance 21847
Performance 380
(e) Demonstrate that this solution gives the minimum cost, and find its value. (6)
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