(a) Formulate this problem as a linear programming problem given that the objective is to maximise the profit made by the quarry per day.

Q1) A boutique can pack and sell two types of gift baskets, each of which contains e2 worth
of soap. Small baskets contain e1 worth of perfumes, and will make e1 of profit each
when sold. Large baskets contain e4 of perfumes and make e3 of profit when sold. The
boutique has e300 worth of soap and e300 worth of perfume to make gift baskets with.
10
(a) Formulate this problem as a linear programming problem given that the objective
is to maximise profit.
15
(b) Using the Graphical Approach, represent the region of feasible solutions and deter-
mine the number of each type of gift baskets which should be produced to maximise
profit. Determine this maximum profit.
15
(c) Confirm this result using the simplex method.
Q2) A company makes 3 different types of electrical circuit board. Each board requires a
certain amount of components, which are listed in the table below, along with the profit
made from the sale of each type of circuit board. The company has only a limited
inventory of each type of component available, the amount of which are also listed in the
table.
Component 1 Component 2 Profit
Board A 4 2 e40
Board B 1 0 e20
Board C 0 2 e20
Inventory 200 600
In addition, the company has determined that it can arrange the sale of at most 500 such
boards at this time.
10
(a) Formulate this problem as a linear programming problem given that the objective
is to maximise profit.
20
(b) Using the simplex method, determine the number of each type of board the company
should make in order to maximise profit, and determine this profit.
MB5014 Problem Solving and Mathematical Modelling Assignment 2: 2016
Q3) A quarry mines raw gravel. A shipment of raw gravel requires 2 hours to load using a
loader and can be sold as is for a profit of e1000 per shipment. The quarry can also
choose to filter gravel using a sifter. A shipment of coarse gravel requires 1 hour of time
on the sifter, takes 1 hour to load, and makes a profit of e2000. A shipment of fine gravel
require 4 hours of sifting, and 2 hours to load, and makes a profit of e6000.
The quarry has a single sifter which can run 24 hours per day, and a single loader which
can only be run for 16 hours a day.
In addition, for tax purposes, each day the number of shipments of raw gravel cannot
exceed the number of shipments of coarse gravel.
10
(a) Formulate this problem as a linear programming problem given that the objective
is to maximise the profit made by the quarry per day.
20
(b) Using the simplex method, determine the number of shipments of each type the
company should make in order to maximise profit, and determine this profit.


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