Page 84 - Mathematics_Form_3

Linear programming
Revision exercise 3
1. The departments of inspection and
evaluation produce two products,
Alpha and Beta. Alpha requires
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2 hours per unit in the inspection
department and 4 hours per unit
in the evaluation department.
Beta requires 3 hours per unit in
the inspection department and 2
hours per unit in the evaluation
department. There are 60 and
80 hours per week available in
the inspection and evaluation
departments, respectively. The
profit per unit for Alpha and Beta
are Tshs 4,000 and Tshs 6,000,
respectively.
(a) Formulate the linear
programming problem
which maximizes the total
production profit.
(b) Use the graphical method to
determine the recommended
product mix.
(c) Find the biggest number of
the Beta product that can be
produced.
2. A manufacturer produces two
different models, X and Y of the
same product. Model X contributes
Tshs 50,000 per unit, while model
Y contributes Tshs 30,000 per
unit towards the total profit. Raw
materials r and r are required
2
1
for production. At least 18 kg of r
1
and 12 kg of r must be used daily.
2
Also, at most 30 hours of labour are
Student\s Book Form Three 77
MATHEMATIC F3 SB.indd 77
MATHEMATIC F3 SB.indd 77
to be utilized. A quantity of 2 kg of
r is needed for model X and 1 kg
1
of r for model Y. For each X and
1
Y, 1 kg of r is required. It takes
2
2 hours to manufacture model X
and 3 hours to manufacture model
Y. How many units of each model
should be produced to maximize
the profit? What is the overall
maximum profit?
3. A certain manufacturing company
has two plants X and Y which
produce nails, nuts, and bolts.
Plant X can manufacture 100 nails,
300 nuts, and 50 bolts at a cost
of Tshs 150,000 per hour. Plant
Y can manufacture 200 nails, 100
nuts, and 50 bolts at a cost of Tshs
200,000 per hour. The company
has received an order of 600 nails,
600 nuts, and 200 bolts. How many
hours should be given to each plant
to satisfy the order at a minimum
cost? What is the minimum cost?
4. A factory manufactures two
types of machines, A and B. To
manufacture a machine of type
A requires 70 kg of alloy metal,
while type B requires 100 kg of
alloy metal. The company can Mathematics for Secondary Schools
use at most 1100 kg of alloy
metal. Machines A and B require
40 minutes and 50 minutes in
the assembling department,
respectively, and the assembling
department has only 600 minutes.
Furthermore, machines A and B
require 18 minutes and 15 minutes,
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