MATH1026 - Coursework 1
Read these notes carefully before submitting the coursework.
Your submission should be a single document in either MS Word or pdf
format. Please note that Moodle will not accept any other format. If you
hand-write your solution you can copy photographs or scanned images of your
work into a Word document and upload it. If you do so, please make sure that
the document displays clearly on a screen when opened.
You need to use the submission link on Moodle to upload the file. This
link will be available until 23h30 on Tuesday 23 March. There is also a late
submission link for anyone who misses the deadline or who has been granted
an extension through extenuating circumstances (ECs). This will only become
usable at 23h30 on 23 March and will work until 23h30 on 6 April. Late submis-
sions will lead to marks being capped unless ECs have been explicitly granted
for this piece of work.
Dick Quibell will be available to answer questions relating to the coursework
at the usual Tutorial and Q&A sessions on 2, 9, 16, 23 March (14h00 to 15h00
and 15h00 to 16h00 via MS Teams), and ad hoc by emailing
Question 1 [45 marks]
Ken and Larry, Inc. produce ice cream of three flavours: chocolate, vanilla
and banana. Ice cream is made of three main ingredients: milk, sugar and
cream. For today’s production 150 pounds of sugar and 60 gallons of cream and
a certain number X of gallons of milk are available. The ingredient requirements
(per gallon of ice cream) are shown in the table below:
Ice Cream Milk (gal) Sugar (lb) Cream (gal)
Chocolate 0.45 0.50 0.10
Vanilla 0.50 0.40 0.15
Banana 0.40 0.40 0.20
Each gallon of made and sold ice cream brings the following net profit figures:
£1.00 for chocolate, £0.90 for vanilla and £0.95 for banana ice cream.
(a) Set up a linear programing problem to determine daily production plan
that maximises total net profit. Clearly explain the meaning of each decision
variable and the meaning of each constraint.
[5 marks]
(b) An experienced manager believes that the best plan would be to produce
only two types of ice cream, not to make the chocolate ice cream at all, and
not to use all available milk. Determine the basic variables. Provided that 20
gallons of milk is not used, apply the transformation matrix technique to setup
1
Read these notes carefully before submitting the coursework.
Your submission should be a single document in either MS Word or pdf
format. Please note that Moodle will not accept any other format. If you
hand-write your solution you can copy photographs or scanned images of your
work into a Word document and upload it. If you do so, please make sure that
the document displays clearly on a screen when opened.
You need to use the submission link on Moodle to upload the file. This
link will be available until 23h30 on Tuesday 23 March. There is also a late
submission link for anyone who misses the deadline or who has been granted
an extension through extenuating circumstances (ECs). This will only become
usable at 23h30 on 23 March and will work until 23h30 on 6 April. Late submis-
sions will lead to marks being capped unless ECs have been explicitly granted
for this piece of work.
Dick Quibell will be available to answer questions relating to the coursework
at the usual Tutorial and Q&A sessions on 2, 9, 16, 23 March (14h00 to 15h00
and 15h00 to 16h00 via MS Teams), and ad hoc by emailing
Question 1 [45 marks]
Ken and Larry, Inc. produce ice cream of three flavours: chocolate, vanilla
and banana. Ice cream is made of three main ingredients: milk, sugar and
cream. For today’s production 150 pounds of sugar and 60 gallons of cream and
a certain number X of gallons of milk are available. The ingredient requirements
(per gallon of ice cream) are shown in the table below:
Ice Cream Milk (gal) Sugar (lb) Cream (gal)
Chocolate 0.45 0.50 0.10
Vanilla 0.50 0.40 0.15
Banana 0.40 0.40 0.20
Each gallon of made and sold ice cream brings the following net profit figures:
£1.00 for chocolate, £0.90 for vanilla and £0.95 for banana ice cream.
(a) Set up a linear programing problem to determine daily production plan
that maximises total net profit. Clearly explain the meaning of each decision
variable and the meaning of each constraint.
[5 marks]
(b) An experienced manager believes that the best plan would be to produce
only two types of ice cream, not to make the chocolate ice cream at all, and
not to use all available milk. Determine the basic variables. Provided that 20
gallons of milk is not used, apply the transformation matrix technique to setup
1
