MA 162 Recitation Worksheet Thursday 10th October 2013
Please attempt as many of the questions as you have time.
Section 3.2
Formulate the following linear programming problems but do not attempt to solve.
(1) Mark Carney plans to invest up to $500, 000 in two projects. Project A yields a return of
10% on the investment and Project B yields a return of 15%. He decides to manage the
risks by investing no more than 40% in Project B. How much should be invested in each
project?
(2) Madison, WI needs at least 10 million gallons of drinking water each day. Their supply
comes from lake Mendota or a pipeline from lake Michigan. Lake Mendota can supply a
maximum of 5 million gallons per day, while the pipeline can supply at most 10 million
gallons per day. The pipeline is contracted to supply at least 6 million gallons each day.
If the cost of 1 million gallons from lake Mendota is $300 and from the pipeline the same
amount costs $500, how much water should come from each source in order to minimise the
cost?
(3) TMA manufactures high definition LED televisions in two separate locations: Smallville
and Bigville. Smallville produces at most 6000 per month, while Bigville makes at most
5000 per month. TMA is the main supplier for the Pulsar Corp. which, requires all its
commitments to be met. This month Pulsar places orders for 3000 televisions to be shipped
to Springfield, IL and 4000 to be shipped to Chicago, IL. The shipping costs are given by:
Smallville
Bigville
Springfield Chicago
6
4
8
10
Determine how to minimise TMA’s shipping costs.
(4) Adam Smith has at most 250, 000 to invest in three mutual funds; a money market fund,
an international equity fund, and an income fund. The money market fund has a return of
6% a year, the equity fund has a return of 10% a year, and the income fund has a return
of 15% each year. Adam wants no more than 25% of his portfolio in the income fund, and
no more than 50% of his portfolio in the equity fund. How much should be in each fund to
maximise his return?
(5) One of the following two problems is a linear programming problem. Decide which one it
is and explain why.
Maximise P = xy
Minimise C = 2x + 3y
subject to 2x + 3y 6 12
subject to 2x + 3y 6
6
2x + y 6
8
x − y =
0
x > 0, y > 0
x > 0, y > 0
1
Section 3.3
(1) Maximize P = 4x + 2y
subject to the constraints
x+y ≤8
2x + y ≤ 10
x≥0
y≥0
(2) A division of the Winston Furniture Company manufactures dining tables and chairs. Each
table requires 40 board feet of wood and 3 labor-hours. Each chair requires 16 board feet of
wood and 4 labor-hours. The profit for each table is $45, and the profit for each chair is $20.
In a certain week, the company has 3200 board feet of wood available and 520 labor-hours
available. How many tables and chairs should Winston manufacture to maximize its profit?
What is the maximum profit?
2