Product A is sold for $1.50 whereas product B is priced at $2.00. There is unlimited demand for
product A but demand for B is limited to 13,000 units per annum. The machine hours available
in each department are restricted to 2,400 per annum. Other relevant data are as follows.
Machine hours required
Mixing
Shaping
Hrs
Hrs
Product A
0.06
0.04
Product B
0.08
0.12
Variable cost per unit
$
Product A
1.3
Product B
1.7
The constraints are:
0.06x + 0.08y ≤ 2,400
0.04x + 0.12y ≤ 2,400
y ≤ 13,000
x,y ≥ 0
The objective function is:
Contribution (C) = 0.2x + 0.3y
The optimal solution is where x = 24,000 and y = 12,000, and total contribution = $(24,000 ×
0.2) + $(12,000 × 0.3) = $4,800 + $3,600 = $8,400.
REQUIRED
Calculate the shadow price of an hour of machining time in shaping department and mixing
department respectively.

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Page
11
of
13
IPK COLLEGE
1664, JALAN KULIM, 14202 BUKIT MERTAJAM, PENANG
TEL : 012-5203212 / 0125113212 / 04-5512588
Subject: Financial Management
(DFM1)
Prepared by Chester Chen
Email : [email protected]
CHAPTER ROUNDUP
All companies have a maximum capacity for producing goods or providing services,
because there is a limit to the amount of resources available. There is always at least
one resource that is more restrictive than others: this is known as a
limiting factor
.
In a situation where a company is able to
sub-contract work to make up a shortfall in
its own in-house production capabilities
, its total costs will be minimised if those
units bought from the sub-contractor have the lowest extra variable cost per unit of
scarce resource saved by buying. Extra variable cost is the difference between the
variable cost of in-house production and the cost of buying from the subcontractor.
Linear programming
is a technique for solving problems of profit maximisation or
cost minimization and resource allocation. 'Programming' has nothing to do with
computers: the word is simply used to denote a series of events. If a scenario contains
two or more limiting factors
, linear programming should be used to determine the
contribution-maximising or cost-minimising solution.
The graphical method of linear programming can be used when there are just two
products (or services). The steps involved are as follows.
(1)
Define the problem:
Define variables
Establish constraints
Construct objective function
(2)
Draw the constraints on a graph
(3)
Establish the feasible region for the optimal solution
(4)
Determine the optimal solution
The
optimum solution
to a linear programming problem can be found by ‘sliding the
iso-
contribution line out’.
The optimal solution to a linear programming problem can also be found using
simultaneous equations
Slack
occurs when maximum availability of a resource is not used.
Surplus
occurs
when more than a minimum requirement is used.
The
shadow price or dual price
of a limiting factor is the increase in value which
would be created by having one additional unit of the limiting factor at its original cost.

___________________________________________________________________________________________________________________
Page
12
of
13
IPK COLLEGE
1664, JALAN KULIM, 14202 BUKIT MERTAJAM, PENANG
TEL : 012-5203212 / 0125113212 / 04-5512588
Subject: Financial Management
(DFM1)
Prepared by Chester Chen
Email : [email protected]

** Subscribe** to view the full document.

- Spring '17
- JANE KDAL